Neuromorphic algorithm for rapid online learning and signal restoration

ABSTRACT

A computer-implemented method of training a neural network to recognize sensory patterns includes obtaining input data, preprocessing the input data in one or more preprocessors of the neural network, and applying the preprocessed input data to a core portion of the neural network. The core portion of the neural network includes a plurality of principal neurons and a plurality of interneurons, and is configured to implement a feedback loop from the interneurons to the principal neurons that supports persistent unsupervised differentiation of multiple learned sensory patterns over time. The method further includes obtaining an output from the core portion, and performing at least one automated action based at least in part on the output obtained from the core portion. The neural network may be adaptively expanded to facilitate the persistent unsupervised differentiation of multiple learned sensory patterns over time by incorporating additional interneurons into at least the core portion.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application claims priority to U.S. Provisional PatentApplication Ser. No. 62/832,071, filed Apr. 10, 2019 and entitled“Neuromorphic Algorithm for Rapid Online Learning and SignalRestoration,” which is incorporated by reference herein in its entirety.

STATEMENT OF GOVERNMENT SUPPORT

This invention was made with government support under Grant Nos. R01DC012249, R01 DC014367 and R01 DC014701 of the National Institutes ofHealth (NIH). The government has certain rights in the invention.

FIELD

The field relates generally to information processing systems, and moreparticularly to processing algorithms implemented in neural networks insuch systems.

BACKGROUND

Machine learning systems for rapid and reliable pattern recognition havea vast plethora of applications, from visual object recognition to airquality control to waste identification to signal detection. Acorrespondingly wide range of machine learning implementations have beendeveloped to address these applications, ranging from traditionalmachine learning algorithms to deep neural networks that are able tolearn and recognize arbitrarily complex patterns via extensive training.The state of the art in deep networks, however, exhibits a number ofwell-known weaknesses that are the focus of intensive study anddevelopment. These include catastrophic forgetting, in which networksrapidly lose their memories for trained exemplars when subsequenttraining is not carefully structured to retain this information (e.g.,via retraining with previous training samples intercalated with the newtraining), vulnerability to adversarial examples in which subtledifferences in inputs can lead to robust misclassification, and limitsto memory capacity in which only a certain number of classes can beconstructed within the network before they begin to interfere with oneanother and degrade performance. Moreover, deep networks are notoriouslyslow to train, and are computationally costly in part because thebackpropagation algorithm that underlies their learning propagates allerror signals back across the entire network. These weaknesses limit theutility of deep learning approaches for many applications, particularlyfield-deployable systems that require rapid learning/adaptation andcannot practically incorporate high-end computational power in theirdesigns.

SUMMARY

Illustrative embodiments provide neuromorphic algorithms for rapidonline learning and signal restoration. For example, some embodimentsmore particularly provide spiking neural network (SNN) algorithms,inspired by olfactory brain circuitry, that enable the rapid onlinelearning of sensor array responses and the subsequent identification ofsource signatures under highly suboptimal conditions. Such embodimentsovercome significant drawbacks of conventional approaches.

In one embodiment, a computer-implemented method of training a neuralnetwork to recognize sensory patterns comprises obtaining input data,preprocessing the input data in one or more preprocessors of the neuralnetwork, and applying the preprocessed input data to a core portion ofthe neural network. The core portion of the neural network comprises aplurality of principal neurons and a plurality of interneurons, and isconfigured to implement a feedback loop from the interneurons to theprincipal neurons that supports persistent unsupervised differentiationof multiple learned sensory patterns over time.

The method in this embodiment further comprises obtaining an output fromthe core portion of the neural network, and performing at least oneautomated action based at least in part on the output obtained from thecore portion of the neural network. A wide variety of differentautomated actions may be taken in different use cases.

In some embodiments, the neural network is adaptively expanded tofacilitate the persistent unsupervised differentiation of multiplelearned sensory patterns over time, illustratively by incorporatingadditional interneurons into the core portion and possibly also into atleast one preprocessor.

The core portion of the neural network in some embodimentsillustratively comprises a synaptic interaction matrix of the principalneurons and the interneurons, in which an n-dimensional representationin the principal neurons is mapped to an m-dimensional representation inthe interneurons, where m>>n.

In some embodiments, the neural network further comprises an inferencenetwork arranged between the principal neurons and the interneurons ofthe core network. The inference network is illustratively configured todeliver input to the interneurons that influences how the interneuronsaffect the principal neurons, such that the principal neurons therebyexert different effects on the interneurons and the inference network.For example, the inference network may be configured to selectivelyactivate certain interneurons. By weakly or partially predicting asolution in this manner, the inference network substantially increasesthe likelihood of successful signal identification by the core networkunder extremely high impulse noise or other highly suboptimalconditions.

These and other illustrative embodiments of the invention include butare not limited to systems, methods, apparatus, processing devices,integrated circuits, and computer program products comprisingprocessor-readable storage media having software program code embodiedtherein.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows an information processing system comprising a processingplatform implementing a neuromorphic algorithm using a spiking neuralnetwork (SNN) in an illustrative embodiment.

FIG. 2 is a combined system and flow diagram showing one possibleimplementation of a neuromorphic algorithm using an SNN in anillustrative embodiment.

FIG. 3 is a schematic diagram showing operation of a neuromorphicalgorithm using an SNN in an illustrative embodiment.

FIG. 4 shows an example of a heterogeneous duplication preprocessor of aneuromorphic algorithm using an SNN in an illustrative embodiment.

FIG. 5A shows a portion of an SNN utilized in implementing aneuromorphic algorithm in an illustrative embodiment.

FIG. 5B shows an example of a processing device implementing aneuromorphic algorithm using an SNN in an illustrative embodiment.

FIG. 5C shows an example deployment scenario of a sensor array in anillustrative embodiment.

FIGS. 6A through 6C illustrate plasticity rules of a neuromorphicalgorithm in illustrative embodiments.

FIG. 7 is a set of graphical plots (a) through (d) showing aspects ofodor learning in illustrative embodiments. The plots are also referredto herein as respective FIG. 7(a) through 7(d).

FIG. 8 is a set of graphical plots (a) through (d) showing aspects ofmulti-odor learning in illustrative embodiments. The plots are alsoreferred to herein as respective FIG. 8(a) through 8(d).

FIG. 9 is a set of graphical plots (a) and (b) showing aspects of odorlearning with plume dynamics in illustrative embodiments. The plots arealso referred to herein as respective FIGS. 9(a) and 9(b).

FIG. 10 is a set of graphical plots (a) through (g) showing aspects ofperformance of a neuromorphic algorithm using an SNN in illustrativeembodiments. The plots are also referred to herein as respective FIGS.10(a) through 10(g).

FIG. 11 is a schematic diagram showing multiple columns of networkcircuitry including an external plexiform layer (EPL) of an SNNimplementing a neuromorphic algorithm in an illustrative embodiment.

FIG. 12 is a combined system and flow diagram showing another possibleimplementation of a neuromorphic algorithm using an SNN in anillustrative embodiment.

DETAILED DESCRIPTION

Illustrative embodiments can be implemented, for example, in the form ofinformation processing systems comprising one or more processingplatforms each having at least one computer, server or other processingdevice. A number of examples of such systems will be described in detailherein. It should be understood, however, that embodiments of theinvention are more generally applicable to a wide variety of other typesof information processing systems and associated computers, servers orother processing devices or other components. Accordingly, the term“information processing system” as used herein is intended to be broadlyconstrued so as to encompass these and other arrangements.

FIG. 1 shows an information processing system 100 implementing aneuromorphic algorithm using a spiking neural network (SNN) in anillustrative embodiment. The system 100 comprises a processing platform102 coupled to a network 104. Also coupled to the network 104 are sensorarrays 105-1, . . . 105-M and controlled system components 106. Theprocessing platform 102 implements at least one neuromorphic algorithm110 and at least one component controller 112. Although this embodimentincludes multiple sensor arrays 105, other arrangements of sensors arepossible, as described elsewhere herein. The term “sensor” as usedherein is intended to be broadly construed, so as to encompass a sensorarray or an individual sensing device of such an array. A sensor as theterm is broadly used herein can itself comprise a set of sensingdevices, such as a sensor array.

Examples of particular implementations of neuromorphic algorithm 110,including a neuromorphic algorithm more particularly referred to hereinas Sapinet, and variants thereof, are described in detail elsewhereherein. The component controller 112 generates one or more controlsignals for adjusting, triggering or otherwise controlling variousoperating parameters associated with the controlled system components106 based at least in part on outputs generated by the neuromorphicalgorithm 110.

The processing platform 102 is configured to utilize an operationalinformation database 114. Such a database illustratively storesoperational information relating to operation of the neuromorphicalgorithm 110 and the controlled system components 106. The controlledcomponents 106 in some embodiments comprise system components that aredriven at least in part by outputs generated by the neuromorphicalgorithm. A wide variety of different types of components can make useof outputs generated by the neuromorphic algorithm 110, such as varioustypes of equipment associated with one or more of the example use casesdescribed elsewhere herein.

The operational information database 114 is illustratively configured tostore outputs generated by the neuromorphic algorithm 110 and/or thecomponent controller 112, in addition to the above-noted operationalinformation relating to operation of the neuromorphic algorithm 110 andthe controlled system components 106.

Although the neuromorphic algorithm 110 and the component controller 112are both shown as being implemented on processing platform 102 in thepresent embodiment, this is by way of illustrative example only. Inother embodiments, the neuromorphic algorithm 110 and the componentcontroller 112 can each be implemented on a separate processingplatform. A given such processing platform is assumed to include atleast one processing device comprising a processor coupled to a memory.

Examples of such processing devices include computers, servers or otherprocessing devices arranged to communicate over a network. Storagedevices such as storage arrays or cloud-based storage systems used forimplementation of operational information database 114 are alsoconsidered “processing devices” as that term is broadly used herein. Insome embodiments, such processing devices comprise one or moreneuromorphic processors.

The network 104 can comprise, for example, a global computer networksuch as the Internet, a wide area network (WAN), a local area network(LAN), a satellite network, a telephone or cable network, a cellularnetwork such as a 4G or 5G network, a wireless network implemented usinga wireless protocol such as WiFi or WiMAX, or various portions orcombinations of these and other types of communication networks.

It is also possible that at least portions of other system elements suchas one or more of the sensor arrays 105 and/or the controlled systemcomponents 106 can be implemented as part of the processing platform102, although shown as being separate from the processing platform 102in the figure.

For example, in some embodiments, the system 100 can comprise a laptopcomputer, tablet computer or desktop personal computer, a mobiletelephone, or another type of computer or communication device, as wellas combinations of multiple such processing devices, configured toincorporate at least one sensor array and to execute a neuromorphicalgorithm for controlling at least one system component.

Examples of automated actions that may be taken in the processingplatform 102 responsive to outputs generated by the neuromorphicalgorithm 110 include generating in the component controller 112 atleast one control signal for controlling at least one of the controlledsystem components 106 over the network 104, generating at least aportion of at least one output display for presentation on at least oneuser terminal, generating an alert for delivery to at least userterminal over the network 104, and/or storing the outputs in theoperational information database 114.

A wide variety of additional or alternative automated actions may betaken in other embodiments. The particular automated action or actionswill tend to vary depending upon the particular use case in which thesystem 100 is deployed. Examples of such use cases are providedelsewhere herein.

The processing platform 102 in the present embodiment further comprisesa processor 120, a memory 122 and a network interface 124. The processor120 is assumed to be operatively coupled to the memory 122 and to thenetwork interface 124 as illustrated by the interconnections shown inthe figure.

The processor 120 may comprise, for example, a neuromorphic processor, amicroprocessor, an application-specific integrated circuit (ASIC), afield-programmable gate array (FPGA), a central processing unit (CPU),an arithmetic logic unit (ALU), a digital signal processor (DSP), orother similar processing device component, as well as other types andarrangements of processing circuitry, in any combination.

As a more particular example, in some embodiments, the processor 120comprises one or more neuromorphic processor integrated circuits.Accordingly, in some embodiments, system 100 is configured to include aneuromorphic processor integrated circuit based processing platform.

As another example, in some embodiments, the processor 120 comprises oneor more graphics processor integrated circuits. Such graphics processorintegrated circuits are illustratively implemented in the form of one ormore graphics processing units (GPUs). Accordingly, in some embodiments,system 100 is configured to include a GPU-based processing platform.

A wide variety of other types and arrangements of processors can be usedin implementing processing platform 102 in other embodiments. The term“processing device” as used herein is therefore intended to be broadlyconstrued, and comprises at least one such processor and at least onememory coupled to the at least one processor.

The memory 122 stores software program code for execution by theprocessor 120 in implementing portions of the functionality of theprocessing platform 102. For example, at least portions of thefunctionality of neuromorphic algorithm 110 and component controller 112can be implemented using program code stored in memory 122.

A given such memory that stores such program code for execution by acorresponding processor is an example of what is more generally referredto herein as a processor-readable storage medium having program codeembodied therein, and may comprise, for example, electronic memory suchas SRAM, DRAM or other types of random access memory, flash memory,read-only memory (ROM), magnetic memory, optical memory, or other typesof storage devices in any combination.

Articles of manufacture comprising such processor-readable storage mediaare considered embodiments of the invention. The term “article ofmanufacture” as used herein should be understood to exclude transitory,propagating signals.

Other types of computer program products comprising processor-readablestorage media can be implemented in other embodiments.

In addition, illustrative embodiments may be implemented in the form ofintegrated circuits comprising processing circuitry configured toimplement processing operations associated with one or both of theneuromorphic algorithm 110 and the component controller 112 as well asother related functionality.

The network interface 124 is configured to allow the processing platform102 to communicate over one or more networks with other system elements,and may comprise one or more conventional transceivers.

It is to be appreciated that the particular arrangement of componentsand other system elements shown in FIG. 1 is presented by way ofillustrative example only, and numerous alternative embodiments arepossible. For example, other embodiments of information processingsystems can be configured to implement neuromorphic algorithmfunctionality of the type disclosed herein.

Terms such as “sensor array” and “controlled system component” as usedherein are intended to be broadly construed. For example, a given sensorarray in some embodiments can comprise multiple sensors collectivelyimplemented on a single common device, or a set ofgeographically-distributed sensors associated with respective distinctInternet-of-Things (IoT) devices. A wide variety of different types ofdata sources can be used to provide input data in other embodiments.

For example, it is possible in some embodiments that a given sensorarray can be replaced with a single sensor. It also is possible in someembodiments that each sensor, embedded within a sensor array, can itselfcomprise a set of multiple physical sensors, with signals generated bysuch multiple physical sensors being combined by averaging, weightedaveraging, or another designated function, prior to being sampled fordelivery to a preprocessor, such that this set of sensors effectivelyacts as a single sensor delivering input data to a single column of aneural network. It further is possible in some embodiments that thisexample association of sets of multiple sensors with respective columnarinputs of the neural network will be computed within one or morepreprocessors, after some preprocessing steps but before otherpreprocessing steps. The term “sensor” as used herein is intended toencompass a device providing input data to a single column of a neuralnetwork, irrespective of how many physical sensors may be combined togenerate this input.

Terms such as “signal restoration” and “signal identification” as usedherein are also intended to be broadly construed, so as to encompass,for example, various arrangements for recognizing a particular sensorypattern given certain input data from a sensor array or other type ofdata source.

Neuromorphic algorithms of the type disclosed herein can be implementedon any platform that can benefit from their rapid online learning andsignal restoration advantages. Such platforms can include any type ofcomputer, mobile telephone, handheld sensor device or other type ofprocessing device that is configured to utilize a neuromorphic algorithmin processing sensory input. It is also possible that a platformimplementing a neuromorphic algorithm as disclosed herein can comprise arobot or other type of automaton. For example, the sensor arrays 105,neuromorphic algorithm 110 and component controller 112 can becollectively configured to provide olfactory functionality for suchentities. These and other aspects of illustrative embodiments disclosedherein are therefore presented by way of example only, and should not beconstrued as limiting in any way.

Additional details regarding illustrative embodiments will now bedescribed with reference to FIGS. 2 through 4.

These embodiments include a particular SNN implementation referred toherein as “Sapinet.” It is to be appreciated that the particularfeatures and functionality of Sapinet as described herein are presentedby way of non-limiting example only, and can be varied in otherembodiments. Sapinet and its variants described below thereforerepresent examples of possible implementations of the neuromorphicalgorithm 110 of FIG. 1. Although Sapinet uses an SNN, it is to beappreciated that other embodiments disclosed herein can implementneuromorphic algorithms using different types of neural networks notnecessarily involving SNNs. Accordingly, use of an SNN in illustrativeembodiments herein should be viewed as exemplary rather than as limitingin any way.

The following description will first introduce each of FIGS. 2 through4, and will then provide additional details regarding the operation ofSapinet in illustrative embodiments.

FIG. 2 illustrates the operation of an example implementation 200 of theSapinet algorithm, which is illustratively used as neuromorphicalgorithm 110 in system 100 in some embodiments. In the implementation200, the Sapinet algorithm includes initial process steps 202 and 204,inputs 203 and 214, one or more preprocessors 205 and a core networkthat includes principal neurons 210, inference network 211 andinterneurons 212. The preprocessor(s) 205 and core network, havingprincipal neurons 210, inference network 211 and interneurons 212,collectively comprise an example of a neural network, and moreparticularly an example of an SNN, in which the Sapinet algorithmexecutes in implementation 200. Such an SNN is also referred to hereinas a Sapinet network.

There are two distinct feedback loops in the implementation 200, denotedas theta and gamma feedback loops in the figure. Theta (θ) indicates theloop governing data sampling; gamma (γ) indicates the faster feedbackloop of the core Sapinet learning/attractor network. Illustrativeembodiments herein implement adaptive network expansion (ANE)functionality. For example, ANE allows new interneurons to be added to aSapinet network to dynamically add capacity without disrupting existingengrams, as illustrated by the solid circular arrow adjacentinterneurons 212 in the figure. ANE can also be deployed in theinference network 211 and in certain preprocessors, as illustrated bythe dashed circular arrows adjacent the corresponding components in thefigure.

The Sapinet network is initialized in initialization step 202, and inputdata is obtained in data sampling step 204. Such operations illustrativeutilize sensory array input and/or numerical data provided via input203. The input data is preprocessed in the one or more preprocessors205, and the preprocessed input data is then applied to the core networkthat include principal neurons 210 and interneurons 212. Theinterneurons 212 may be configured in accordance with priors via input214.

The inference network 211 is arranged between the principal neurons 210and the interneurons 212 within the core network and is illustrativelyconfigured to deliver input to the interneurons 212 that influences howthe interneurons 212 affect the principal neurons 210, such that theprincipal neurons 210 thereby exert different effects on theinterneurons 212 and the inference network 211.

As indicated above, the core network in this embodiment implements thegamma feedback loop from the interneurons 212 to the principal neurons210. This gamma feedback loop is an example of what is more generallyreferred to herein as a feedback loop that supports persistentunsupervised differentiation of multiple learned sensory patterns overtime, as will be described in more detail elsewhere herein.

The gamma feedback loop in some embodiments is configured to controldelivery of synaptic inhibition information from the interneurons 212back to the principal neurons 210 of the core network, illustrativelybased at least in part on synaptic excitatory information delivered fromthe principal neurons 210 to the interneurons 212.

The theta feedback loop is an example of what is more generally referredto herein as a data sampling loop, and is utilized in obtaining inputdata for the one or more preprocessors 205. Multiple cycles of the gammafeedback loop are illustratively executed within a single cycle of thetheta feedback loop.

The input data in implementation 200 can be obtained, for example, fromone or more sensor arrays or other arrangements of sensors, via input203, using the data sampling step 204 with timing controlled by thetheta feedback loop.

Outputs are illustratively obtained from the core network, includingreadouts from the principal neurons 210, the inference network 211 andthe interneurons 212, with such readouts being denoted as Readout #1,Readout #2 and Readout #3 in the figure. Various automated actions maybe taken based at least in part on these and other outputs ofimplementation 200, also as described elsewhere herein.

In the FIG. 2 embodiment, the SNN is configured to provide spike timingfor the gamma feedback loop, with inhibition delaying the spike timingand relatively strong sensory input advancing the spike timing.

Operation of the gamma feedback loop in adapting synaptic weights of thecore network is illustratively controlled based at least in part onspike timing information represented by relative timing of spikes for atleast a portion of the principal neurons 210 and the interneurons 212.

In some embodiments, at least a subset of the principal neurons 210 ofthe core network are configured to represent respective mitral cells(MCs) of an olfactory learning system and at least a subset of theinterneurons 212 of the core network are configured to representrespective granule cells (GCs) of the olfactory learning system,although numerous other arrangements are possible, and the disclosedarrangements should therefore not be viewed as being restricted toolfactory learning applications. MCs are therefore considered examplesof what are more generally referred to herein as principal neurons orPNs, and GCs are considered examples of what are more generally referredto herein as interneurons or INs. Other types of principal neurons andinterneurons can be used in other embodiments.

As indicated above, the SNN of implementation 200 can be adaptivelyexpanded by incorporating additional interneurons 212 into the corenetwork, and additionally or alternatively by incorporating additionalinterneurons into the inference network 211 and/or at least one of theone or more preprocessors 205.

In some embodiments, the additional interneurons 212 are advantageouslyincorporated into the core network in a manner that does not disruptexisting learned sensory patterns of the core network.

Additionally or alternatively, the SNN of implementation 200 can beconfigured to provide a neuromodulatory dynamic state trajectoryconfigured to adjust neuronal properties systematically and select aparticular outcome.

These and other features of illustrative embodiments will be describedin more detail below.

Referring now to FIG. 3, a portion 300 of the Sapinet implementation 200is shown in more detail. Sensor inputs received via input 203 andsampled in data sampling step 204 are filtered through the one or morepreprocessors 205 and cause excitation of principal neurons 210 of thecore network, which are illustratively MCs and are shown as triangles inthe figure. These excitatory principal neurons 210 form a synapticinteraction matrix 302 in the core network with inhibitory interneurons212 of the core network, which are illustratively GCs and shown as ovalsin the figure. In this figure and elsewhere herein, the principalneurons 210 are also referred to as PNs, and the interneurons 212 arealso referred to as INs. The one or more preprocessors 205 in thisembodiment are associated with a glomerular layer (“GlomL”) as shown.Details of such a layer are described in more detail elsewhere herein.

The synaptic interaction matrix 302 of the principal neurons 210 and theinterneurons 212 in the present embodiment illustratively comprises ann-dimensional representation in the principal neurons 210 which ismapped to an m-dimensional representation in the interneurons 212, wherem>>n. The synaptic interaction matrix 302 is also referred to in thefigure as characterizing a plastic network.

The horizontal lines near the principal neurons 210 at the left side ofthe figure denote lateral dendrites of those principal neurons 210, andthe particular intersections marked with a dot denote the branch pointsof an MC dendritic tree. The inset in the figure depicts suchinterconnections as represented by the synaptic interaction matrix 302,in which intersecting lines have some initial probability of beingconnected to each other (e.g., 20%). During training, the weights ofthese synaptic interactions are iteratively modified over multiplelearning cycles corresponding to respective gamma cycles of the gammafeedback loop of FIG. 2. During testing/classification, the pattern oflearned weights in the synaptic interaction matrix 302 mediates anattractor network. Representations can be read out from principalneurons 210, via Readout #1 of FIG. 2, or from interneurons 212, viaReadout #3 of FIG. 2. The inference network is not depicted in FIG. 3.

Additional details relating to illustrative embodiments of the one ormore preprocessors 205 will now be described.

A given one of the one or more preprocessors 205 illustrativelycomprises a plurality of input nodes, each adapted to receive input dataassociated with a different data source. For example, the input nodesmay be adapted to receive input data from respective different sensorsof a sensor array. In some embodiments, each input node may receiveinput data from a data source comprising any number of physical sensors.

In some embodiments, the given preprocessor more particularly comprisesa heterogeneous duplication preprocessor configured to statisticallyregularize diverse sensory inputs of the obtained input data.

As a more particular example, the given preprocessor may comprise, for aparticular one of the input nodes, a plurality of excitatoryfeed-forward interneurons each coupled to the particular input node, anda plurality of principal neurons each coupled to one or more of theexcitatory feed-forward interneurons.

FIG. 4 shows a schematic of a heterogeneous duplication preprocessor 400in one embodiment. In this embodiment, each sensor stream from a giveninput sensor 402-1 is fanned out to a set 404 of multiple excitatoryfeed-forward interneurons, each of which projects sparsely and randomlyto a number of “sister” principal neurons in a set 406 of principalneurons. Here, the number of principal neurons N is 5*C, where C is thenumber of input sensors; this number can vary, and some variations ofthis architecture have individual principal neurons receiving input frommore than one sensor. Also, as indicated previously, the term “sensor”as used herein is intended to be broadly construed, and can in someembodiments include a set of multiple physical sensors. It should benoted that the cellular properties of the interneurons and principalneurons, and the weights of the synaptic projections, are heterogeneous.When implemented following sensor scaling and global normalization, thispreprocessor 400 serves to statistically regularize diverse sensoryinputs. Outputs of the preprocessor 400 are provided to the core networkas illustrated in the figure. In some embodiments, at least portions ofthe principal neurons 406 are considered part of the core network ratherthan part of the preprocessor 400.

In the FIG. 4 embodiment, the brain-mimetic implementation ofheterogeneous duplication of the preprocessor 400 is modeled afteraspects of the intraglomerular circuitry of the mammalian main olfactorybulb (MOB), and serves to statistically regularize the distribution ofamplitudes among inputs. Each sensor input is delivered to a number ofexcitatory feedforward interneurons (here, five) comparable to theexternal tufted (ET) cells of the MOB, and from there, via sparse,random, feedforward projections, to the principal neurons of the corelearning network (analogous to MOB MCs). This example preprocessorconfiguration illustratively expands the size of the core learningnetwork; here, each sensor now corresponds to a column with fivecomputing units/sister MCs.

Additional details relating to illustrative aspects of Sapinet and itsvariants will now be described.

SNNs, also known as neuromorphic networks, comprise an alternative totraditional analogue-valued deep networks. Like traditional deepnetworks, they are based on a neuroscience metaphor, comprising a largenumber of state variables (“neurons”) coupled pairwise by transferfunctions (“synapses”). Unlike deep networks, the communication betweenneurons is based on discrete spikes (also referred to as events, orpulses); accordingly, they sometimes have been referred to these aspulsed, pulse-coupled, or event-based networks. In principle, spikingnetworks have universal computational power—that is, they aretheoretically capable of computing any algorithm. However, SNNs also canbe constructed with specific architectures, as is observed in the brain,thereby favoring improved effectiveness at certain tasks at the cost ofgenerality (i.e., the architecture is part of the algorithm). Thisneuromorphic principle can be extended to incorporate multiple differentneuronal and synaptic types, feedback loops, sparse connectivity,localized synaptic learning rules, and other heterogeneities that aregenerally not considered in traditional deep learning systems.

When implemented on appropriate hardware, SNNs are extremely energyefficient and uniquely scalable to very large problems; consequently,marrying the efficiency of neuromorphic processors with the algorithmicpower of deep learning is an important industry goal.

The theoretical promise of SNNs has motivated the development ofmultiple neuromorphic hardware platforms, including the academicplatforms SpiNNaker and BrainScaleS, as well as IBM's TrueNorth platformand, most recently, the Loihi platform of Intel Labs, which embedsrapid, iterative plasticity (“self-learning”) in a compact, scalablechip. These hardware platforms are considered illustrative examples ofwhat are more generally referred to herein as “processing devices” or“processing platforms.” A premise of these hardware projects is that theavailability of these platforms would spur the development of practical,useful neuromorphic algorithms by highlighting their particularstrengths in energy efficiency and scalability.

Illustrative embodiments such as Sapinet provide significantimprovements over conventional techniques. Such conventional techniquesinclude the following:

1. Traditional deep learning/deep neural networks (DNNs). This is a vastfield of research with powerful applications. These networks aregenerally unstructured a priori and can learn nearly any patterns givenenough training. However, training is very slow (thousands to millionsof iterations), and updating (“learning”) depends on a globalbackpropagation rule that requires highly interconnected (andcorrespondingly slow) networks. SNNs have many fewer currentapplications, and none to our knowledge that are currently commerciallyimportant. Rather, SNNs are competing with DNNs on the basis of theirlower energy expenditure and ability to be deployed on specializedhardware (like the Intel Loihi or IBM TrueNorth). Additionally, SNNs aremost effectively competing with DNNs by implementing customarchitectures that are specialized for certain applications (“thearchitecture is part of the algorithm”). Sapinet is taking thisapproach, and comparisons against a contemporary DNN are illustrated inFIG. 10. Briefly, Sapinet exhibits few-shot learning, online learning(lack of catastrophic forgetting), and other features that DNNs do notexhibit. Some specialized DNNs are working to limit catastrophicforgetting by slowing/freezing certain weights after learning a givenstimulus, so that that stimulus will not be forgotten after subsequentlearning of other stimuli. However, success in this approach is stilllimited, and a great deal of supervision is required to identify andstabilize the more important weights. In short, SNNs like Sapinet arefar superior to DNNs for a limited range of problems. The rapidlearning, rapid updating in response to sensor drift, and energeticallyefficient hardware implementations are the most substantive and relevantadvantages of Sapinet and some other SNNs over potential DNNcompetitors.

2. Other SNN implementations. Echo state networks and liquid statemachines are the state of the art in the theoretical description of thecapabilities of SNNs. Compared to Sapinet, however, these networkseschew specific architectural designs in favor of exploring theuniversal computational capabilities of SNNs. In this way, theseapproaches are more directly comparable to the state of the art in DNNs.Sapinet, in contrast, has instantiated nonplastic structure inspired bythe neural circuitry of the mammalian olfactory system. Accordingly,Sapinet excels at problems that resemble the problem of odor learningand identification. Fortunately, this problem structure is quite broad,and includes many non-chemosensory applications. Specifically, Sapinetis applicable to any problem based on the classification of inputpopulations that do not exhibit relevant low-dimensional structure, suchas the two-dimensional patterns of a visual image. Additionaldescription elsewhere herein provides particular use cases inillustrative embodiments. Such use cases can involve taking variousautomated actions based at least in part on Sapinet outputs.

3. Other ways of analyzing chemosensory data (machine olfaction,artificial nose research). Conventional machine olfaction essentiallycomprises that portion of the chemosensors market that is focused onlarge arrays of broadly sensitive sensors (see, e.g., K. C. Persaud etal., “Neuromorphic Olfaction,” CRC Press, Boca Raton, Fla. 2013),sometimes including processes of environmental adaptation or learning.Most machine olfaction research uses traditional machine learningapproaches; these approaches are outclassed by Sapinet. There also is asmall but interesting literature concerning biologically inspiredalgorithms of modest complexity. Several emphasize concentrationtolerance, as that is one of the simplest problems to resolve undertheoretical no-noise conditions. Two such algorithms are based on thepremise that the rank order of spike latencies following stimulus onsetis concentration-invariant, and hence can recognize odors acrossconcentrations. There is some truth to this principle, though it fallsapart at lower or higher concentrations where individual sensorresponses begin to asymptote, and there is no provision for recognitionunder noise. Several other biomimetic models emphasize the utility ofdecorrelation using lateral inhibition, though these networks largelyignore the dimensionality problems that nonplastic lateral inhibitionpresents in such systems. Some other biomimetic models are based onhigher-dimensional projections using Hebbian learning (roughlycomparable to the feed-forward component of the Sapinet core network),after which linear classifiers are used; however, these approaches lackfeedback and do not develop or utilize properties comparable to thek-order receptive fields of interneurons in Sapinet. A more recentHebbian plasticity-based model achieves rapid, few-shot odor learningand explores the utility of sparse representations, but is based onspike rates and primarily oriented towards exploring the controlpossibilities of the neuromodulator octopamine in insects. Some modelsinclude dynamics—e.g., oscillations comparable to Sapinet's gammanetwork, as these oscillations are prominent in mammalian and insectolfactory systems; however, oscillations and spike synchrony are notdirectly functional, and are not applied towards enhancingclassification performance. Other work using SNNs for odorclassification is limited to proofs of concept that higher-dimensionalprojections coupled with simple plasticity rules can quickly generaterobustly distinct representations. Although this principle is wellestablished, and is utilized in some embodiments herein, conventionalapproaches remain underdeveloped for practical, real-world applications.

Unique to Sapinet are the use of gamma oscillations as a clock tomeasure spike latencies and establish attractor dynamics, and thedeployment of feedback network inhibition to delay, rather than prevent,principal neuron spike times. Sapinet establishes the principle of thepermanent, unsupervised differentiation of interneurons, and supportslifelong learning owing to its ANE functionality. Sapinet has beendeveloped to the point where the statistical unreliability of naturalsignals has been recognized as a challenge to the network, and resolvedwith cascades of preprocessors (the exception is concentrationtolerance, a problem that has been solved several times as noted above).Sapinet uses sophisticated parameters for its excitatory learning rulesto regulate the value of k, and uniquely includes inhibitory learningrules. No other approach to date has developed or even proposed theinclusion of the functions of the Sapinet inference network, or of theneuromodulatory sweep. Indeed, only Sapinet has been explicitly testedfor recognition and classification performance under high levels ofnoise. Finally, Sapinet also is being developed in concert with ananalytical mathematical framework that underlies its approach tohierarchical classification and supervised perceptual learning.

The uniqueness of Sapinet is not primarily in specific unique featuresor algorithmic strategies, though it does include several of each.Rather, Sapinet is a robust and well-vetted system that, because of itsinclusion of several layers of processing intended to solve multiplepractical problems of learning and recognition, has achieved strongperformance under realistically problematic circumstances.

Accordingly, there are multiple illustrative embodiments disclosedherein exhibiting different instantiations of Sapinet's core principles.For example, as described below, the excitatory synaptic learning ruleserves to develop increasingly specific experience-dependent receptivefields in interneurons (e.g., GCs), whereas the inhibitory synapticlearning rule serves to denoise representations in principal neurons(e.g., MCs). The specific implementations and parameters of these rules,however, differ among illustrative embodiments, particularly dependingon factors such as the hardware platform on which they are instantiated.For example, different instantiations of the excitatory learning rule,with associated parameters, are described for x86 architectures in someembodiments herein, whereas the same rule in a form compatible with theLoihi neuromorphic chip instruction set is described in conjunction withother embodiments herein. Moreover, there are multiple sources of noise(e.g., error) that Sapinet is designed to identify and disregard. Eachof these is described separately below, in some cases in conjunctionwith different illustrative embodiments, but examples include (1) random(Gaussian) noise, (2) variance arising from odor plume dynamics, (3)variance arising from unregulated odor concentration (or other signalintensities), (4) variance arising from unpredictable sensor drift, and(5) impulse (Bernoulli) noise arising from competitive interference(e.g., background odors/signals) that effectively randomize theresponses of a proportion of the sensors.

In the following, we describe in detail certain illustrative embodimentsof a SNN-based algorithm for signal restoration and identification(classification) that we refer to herein as Sapinet (FIGS. 2 and 3).

Sapinet is based on architectural and computational principles extractedfrom the neural circuitry of the mammalian olfactory system. It isdesigned for the rapid learning of arbitrary, high-dimensional patternsand the subsequent recognition and classification of such patterns inthe presence of high levels of interference (for example, in which anunknown 60% of the sensors return random, noninformative values, and/orall sensor response profiles have drifted, and/or signal intensities arefluctuating unpredictably). Specifically, Sapinet is broadly applicableto input derived from arbitrary sensor arrays (including heterogeneousarrays of sensors) or arbitrary lists of features (such as a set ofcellular characteristics derived from a breast cancer biopsy). For thesepurposes, Sapinet's performance is superior to deep network-basedalternatives within most realistic, deployable scenarios—in particular,those in which limited computing power is immediately available, or thatdo not permit indefinite periods of training and retraining (e.g., seeFIG. 10). Unlike deep networks, Sapinet also is capable of robust onlinelearning, in which new patterns can be learned, and the size of thenetwork can be dynamically expanded, without impairing the network'smemory for patterns already learned. Sapinet can be much more rapidlytrained than a deep network—often requiring only one- or few-shottraining to learn to robustly recognize patterns embedded within copiousnoise. Unlike generically trained networks, Sapinet explicitly embedsrepresentations of similarity (e.g., intrinsic quantification of thesimilarity of different inputs), which counteracts the effectiveness ofadversarial examples and enables generalization beyond experience.Representations are based in part on spike timing properties, enablingthe fast and unambiguous communication and computation of information bythe SNN. Finally, plasticity in Sapinet is based on local synapticlearning rules, and hence takes advantage of the optimizations ofspecialized neuromorphic hardware platforms (in particular, thecolocalization of memory and compute). An implementation of Sapinet onthe Intel Loihi neuromorphic hardware platform is described elsewhereherein with reference to FIGS. 5 through 10.

Illustrative implementations of Sapinet are not designed for visualimages or other signals in which embedded low-dimensional information iscritical (e.g., ImageNet, MNIST), and is not expected to be competitivefor visual classification problems in its present form. Rather, it isappropriate for pattern recognition in any dataset comprised ofunstructured lists of input or sensor values, such as genomics datasets,microarrays, sets of medical diagnostic criteria, band-discretizedspectral signatures, and chemosensor arrays. With the inclusion of theappropriate preprocessors, Sapinet can accept as input any arbitrarysets of values or can be connected to any arbitrary battery of sensorsthat can provide a numerical representation of their activity to thenetwork.

Accordingly, a wide variety of different sensors can be used inillustrative embodiments herein, including any sensor that can provide asignal or other numerical representation to the network. Suchrepresentations can include, for example, voltage values, currentvalues, resistance measurements, as well as many other variants withoutlimitation. Examples of sensors that can be used in illustrativeembodiments herein include numerous different types of chemical sensorsand/or gas sensors as well as other types of sensors, including, in someembodiments, image sensors. It is therefore to be appreciated that theterm “sensor” as used herein is intended to be broadly construed, and asindicated elsewhere herein, such a sensor can itself comprise a sensorarray having multiple physical sensors. These and other sensors cancomprise or otherwise be implemented in, for example, IoT devices,mobile devices, and a wide variety of other types of processing devices.

As indicated previously, an example Sapinet implementation 200 isdepicted in FIG. 2. A network is constructed and initialized based onthe size of the input (sensor) array as well as on other user-dependentcriteria. Sensor array input (or an equivalent vector of input values)is presented to the network; the input to each sensor can be a singlevalue, a list of values (e.g., sampled in turn according to the “theta”cycle) or a continuous sensory stream (e.g., sampled at discreteintervals according to the “theta” cycle). Each input sample vector isfiltered through a set of preprocessors for signal conditioning.Ultimately, preprocessor output is delivered to the complement ofprincipal neurons (PNs) that comprise part of the core attractornetwork. (Each sensor's activity may be ultimately mapped onto a singlePN, or may be mapped onto a different number of PNs by one of thepreprocessors).

The core network projects PN activity onto a larger number ofinterneurons (INs), activating them such that they, in turn, deliversynaptic inhibition back onto the PN array. The weight matrix betweenPNs and INs (FIG. 3) is initially sparse (i.e., only a fraction of thepossible connections between PNs and INs actually exist), and becomessparser and more selective with learning. During sensory activation,this excitatory-inhibitory feedback loop is driven through severalrecurrent cycles (the gamma cycle). When learning is active, synapticweights at the excitatory (PN→IN) and inhibitory (IN→PN) synapses areupdated over successive gamma cycles according to local learning rules.During testing, successive gamma cycles underlie an attractor network inwhich these learned synaptic weights shape the attractor state, leadingto pattern recognition even under highly noisy conditions.

An inference network can be included in a Sapinet instantiation,receiving a copy of PN activity and delivering its output onto INs inparallel to direct PN→IN excitation. When present, the inference networkprovides additional pattern completion capacities, and embeds additionalmemory that can be deployed to select among competing engrams so as toenable the (sequential) recognition of multiple knowns within a singlesample. (The latter effect also can be achieved by externally imposedpriors, also generally delivered onto INs, as illustrated in FIG. 8(d)).Lastly, inference networks can be used to govern more sophisticatedlearning methods (e.g., odor learning methods, etc.), enabling, forexample, experience-based changes to the intrinsic discriminability ofsimilar inputs with different implications (perceptual learning).Briefly, by selectively deploying inhibition in service to the need toincrease the discriminability of two similar inputs (e.g., physicallysimilar inputs, chemically similar inputs, etc.), their representationsin the network can be permanently driven apart.

Finally, Sapinet is capable of “lifelong learning”—summarized as thecapacity to keep learning new patterns indefinitely. Online learning—theability to learn new patterns as they occur, without disrupting earlierlearning—also is implicit in lifelong learning. To do this, Sapinetdynamically expands the number of interneurons via ANE, as illustratedin FIG. 2. It should be noted that ANE does not disrupt existingmemories and does not require parameter adjustments to maintainperformance. This capacity for online/lifelong learning also can be usedto counteract sensor drift. ANE also can be deployed in the inferencenetwork and in certain preprocessors.

This combination of biomimetic features constitutes a new SNN-basedalgorithm for pattern learning and recognition under noise that iscompetitive in performance with state-of-the-art deep networks whilealso exhibiting clearly superior practical properties such as veryrapid, lifelong learning, a robustness to widely variable input signals,resistance to catastrophic forgetting, and compatibility with dedicatedneuromorphic hardware platforms.

Sapinet is an SNN algorithm, which is an example of what is moregenerally referred to herein as a neuromorphic algorithm. SNNs ingeneral, and Sapinet in particular, are based on several core principlesthat differentiate them from contemporary deep neural networks:

1. Event-based architecture, by which communications between neurons aremediated by discrete pulses, or spikes, as opposed to direct analoguevalues. This has some advantages in embedded systems, because it favorsvery low-power implementations and is not susceptible tomiscommunications based on environmental factors such as ambienttemperature.

2. Neurons and synapses are not necessarily uniform; they can be ofmultiple types and exhibit arbitrarily different computationalproperties. In Sapinet, for example, principal neurons (PNs) excite theneurons that they target, whereas interneurons (INs) are inhibitory.Neurons may act as strict integrators, leaky integrators, or exhibitmore complex responses to input. They may also exhibit other internalstructure; for example, in some implementations, Sapinet PNs have twocompartments that follow different rules, but work in concert to producea common output (e.g., as described elsewhere herein regarding anillustrative embodiment on the Loihi chip). Additionally, the density ofsynaptic connections among neurons in SNNs often is much sparser than iscommon in deep networks.

3. Network architectures are not necessarily feed-forward; they caninclude any number of feedback loops. Feedback-inclusive spikingnetworks are sometimes referred to as recurrent neural networks (RNNs),examples of which include echo state networks and liquid state machines.Recurrent networks may exhibit dynamical systems properties, such asSapinet's gamma cycle (FIG. 2).

4. Information can be highly localized, such that synaptic learningrules may depend only on local interactions without reference to globalnetwork state. This enables SNNs to take advantage of the benefits ofthe “colocalization of memory and compute,” a core efficiency principleof neuromorphic hardware whereby memory resources can be effectivelylocalized across a physical network. The corresponding constraint isthat computations at particular synapses will not have global access toinformation about network state.

5. While general reservoir computing SNN models can be as generic andpluripotent as traditional deep networks, the architecturalnon-uniformities described above imply that some aspects of networkarchitecture may be predesigned and application-specific. Particular SNNdesigns therefore favor some capabilities at the expense of others, asrepresented by the principle that “the architecture is part of thealgorithm.” These may include multiple computational layers comprised ofdifferent network elements that process signals sequentially orrecurrently. Sapinet is designed around a specific layered architecturethat enables its fast learning and robust classification-under-noiseperformance, at the expense of its generality.

6. SNN models are capable of processing continuous-time inputs,discretely sampled by a network's internal dynamics (e.g., Sapinet'stheta cycle; FIG. 2).

As illustrated in FIG. 2, Sapinet comprises a set of one or more inputpreprocessors, a core SNN of sparsely coupled excitatory and inhibitoryneurons, and a set of supervisory and storage systems that regulate thecore SNN. These supervisory systems may be fully instantiated networksor simple, task-specific control mechanisms. Each of these components isillustrated in FIG. 2 and described below.

With regard to input 203, which illustratively comprises sensor arrayinput and/or numerical data, Sapinet can accept as input any arbitraryset of C values, presented in parallel, or can be connected to anyarbitrary battery of C sensors. Sapinet will periodically sample thestate of these sensors in data sampling step 204 at a frequencycontrolled by the theta feedback loop. Each sample may be, for example,a simple reading, an average, or a weighted average over time. Samplesthat are averaged across a timespan can improve performance by reducingrandom sampling error noise.

In the initialize network step 202, Sapinet will construct a new networkat initialization based on user-specified parameters. In particular, thenew network typically will be initialized with a number of principalneurons N equal to or larger than the number of sensor inputs C. Any orall of the available preprocessors 205 may be included in the newlyinitialized network. Note that some of these preprocessors 205 streamindividual sensor inputs to multiple principal neurons; additionally,individual principal neurons may receive input from just one sensor orcombine inputs from multiple sensors. Accordingly, the selection ofpreprocessors and their parameters, together with the number of sensorsC, determines the number of principal neurons Nin the newly initializednetwork.

The nonplastic hyperparameters of a newly instantiated network and theinitial conditions of plastic parameters are tuned to the structure andscale of the network and the statistical structure of the inputsintended to be delivered to the core network of FIG. 2. Preprocessors205 are utilized to ensure that arbitrary sensor input patterns aresystematically conditioned to adhere to the requirements of the corenetwork; this ensures that Sapinet can productively respond to anyarbitrary input profile (this is referred to as the capacity for“learning in the wild”).

Different types of preprocessors 205 can be instantiated in any givennetwork. These range from simple signal conditioning algorithms tospecialized network components comprising additional neuron types (e.g.,ET neurons, periglomerular (PG) neurons) and synaptic connectionpatterns that are embedded into the network during initialization.

The core network of Sapinet comprises principal neurons 210,interneurons 212, and (optionally) an inference network 211 organized ina gamma feedback loop. This gamma feedback loop is periodic and exhibitsan intrinsic processing frequency called the gamma cycle. Multiple gammacycles (e.g., five) are embedded within each data sample period(successive samples are taken at the slower theta frequency as describedabove). During test sampling, these gamma cycles underlie attractordynamics that enable the network to identify trained patterns undernoisy conditions. Sapinet can also deliver a “none of the above” resultbased on a user-specified level of certainty.

The core network is initialized with a sparse degree of connectivityfrom principal neurons 210 to interneurons 212; this connection densityis a parameter of interest but a 10-20% random connectivity is typical.If an inference network is present, the connection densities fromprincipal neurons 210 to the inference network input layer and from theinference network output layer to interneurons 212 are similarly sparseand random at initialization. In contrast, the connections frominterneurons 212 onto principal neurons 210 are specific and determinedat initialization, generally with an equal, or roughly equal, number ofinterneurons set up to synaptically inhibit each principal neuron.Interneurons are individually limited in the number of principal neuronsthat they inhibit; the specific number is a parameter of interest.

The principal neurons 210 integrate sensor information followingpreprocessing, and emit spikes (events, pulses) as output. There aremultiple specific implementations, but they share the property ofspiking earlier within each gamma cycle in proportion to the strength ofthe sensory input that they are receiving. (This “phase precedence code”bypasses a common flaw of SNNs in which values are communicated via meanspike rates, hence requiring substantial time and energy to be spent ona statistically reliable period of firing in order for downstreamnetwork elements to measure the mean rate). Earlier spikes areinterpreted as stronger signals for pattern recognition (Readout #1),and also are delivered to interneurons (and to the inference network 211if present). The plasticity rule for excitatory neuronal projections issensitive to relative spike timings on the gamma scale, such thatinterneurons and the inference network input layer will adapt theirreceptive fields to principal neuron input during learning.

The interneurons 212 receive synaptic excitation from principal neurons210. As noted above, each interneuron initially receives input from arandomly selected proportion of principal neurons (e.g., 20%) drawn fromacross the entire principal neuron population. Interneurons spike when asufficient number of their presynaptic principal neurons fire (thisnumber is illustratively the interneuron receptive field order k, and,in some embodiments, will vary among interneurons), and an excitatorysynaptic plasticity rule strengthens those inputs from the principalneurons that caused the interneuron to fire and weakens the otherinputs. This progressively narrows the field of effective inputs to asmall number of principal neurons k, where the order k depends onfactors such as the inhibitory neuron's spike threshold and the limit onthe maximum excitatory synaptic weight. Hence, individual interneuronslearn to become responsive to diagnostic feature combinations of orderk. They deliver their activity as inhibition onto principal neurons,where it serves to delay principal neuron spike firing according to theinhibitory synaptic weight. This weight is determined by one of a set ofinhibitory synaptic learning rules that depend on the structure of thenetwork and the presence of an inference network. The effects of thissynaptic inhibition on principal neurons causes them to fire atdifferent times in the next gamma cycle, thereby activating a differentpopulation of interneurons and evoking recurrent activity that exhibitsattractor dynamics.

The core network in some embodiments is illustratively constructed withneuron populations exhibiting heterogeneous properties (such asthresholds, initial synaptic weights, and maximum synaptic weights).Heterogeneous properties across the interneuron population ensures thatdifferent interneurons will exhibit different values of k, such thatsome interneurons are responsive to relatively common low-orderdiagnostic feature combinations and others are responsive only to rarer,higher-order diagnostic feature combinations. Heterogeneous propertiesamong the principal neuron population can influence the particularpopulations of principal neurons that will constitute effective inputsto interneurons, and also contributes to the efficacy of theheterogeneous duplication preprocessor, as described elsewhere herein inconjunction with heterogeneous duplication features of illustrativeembodiments.

The plastic network of the core feedback loop, consequently, is based ona simple matrix of excitatory-inhibitory interactions (FIG. 3). Animportant aspect of the Sapinet algorithm in some embodiments is in thelocal learning rules that govern changes in these synaptic weights, andin the emergent properties that these learning rules engender, as willbe described in more detail elsewhere herein. Sapinet natively performsfew-shot online learning, and can be trained in a semi-supervised orunsupervised mode (with post hoc labeling). More sophisticatedinstantiations can learn correspondingly more sophisticatedrepresentations. The SNN framework in which Sapinet is constructedfurther enables its instantiation on neuromorphic hardware such as theIntel Loihi research chip. This is of particular value because Sapinetbenefits from the dimensionality inherent in large numbers of sensors(e.g., to limit background interference under high-noise conditions),even when these sensors are not individually characterized.Specifically, it does not suffer from the “curse of dimensionality”(i.e., geometrically increasing computational load as dimensionalityincreases) when implemented on appropriate hardware such as the Loihichip (FIG. 5B).

With regard to the preprocessors 205, neural networks typically requirewell-behaved input data. Specifically, nonplastic networkhyperparameters are generally optimized for particular ranges anddistributions of input amplitudes, and the network may perform poorly ifthese limits are violated. For example, mean input values that are muchlarger or smaller than the optimized range will often drive a network'sstate into uninteresting cul-de-sacs, whereas input values that are toounbalanced in their amplitudes can lead to overtraining on the strongerinputs while failing to train on weaker inputs, thereby impairing thenetwork's ability to learn the structure of the input data. For anetwork to operate smoothly on unprocessed, real-world datasets,preprocessor algorithms are needed to automatically transform theresulting inputs into a form palatable to the network without losing thecritical information that they contain. We have developed several suchalgorithms, as disclosed herein, any or all of which may be applied toraw input data (whether numerical or from sensor arrays) beforepresentation to the core Sapinet network.

One example of a preprocessor that is utilized in illustrativeembodiments herein is a heterogeneous duplication preprocessor of thetype illustrated in FIG. 4, as will now be described in more detail.

Ordinal forcing solves the input-distribution problem, but it losesuseful information about the relative amplitudes of sensory inputs. Toreplace this, we developed a statistical regularization method thatachieves the same outcome by employing two layers of input neurons withheterogeneously-weighted synapses, corresponding roughly to a matrixmultiplication with randomized weights (FIG. 4). Specifically, withineach column, sensors project to a heterogeneous set of excitatoryfeed-forward interneurons, rather than directly activating principalneurons. These excitatory neurons then project in turn (sparsely andrandomly) to a heterogeneous set of principal neurons; the weights ofthese projections also are heterogeneous. The effect of thistransformation (following sensor scaling and global normalization) is tostandardize the distribution of activation levels across the incomingsensory streams, improving the capacity of the network to perform wellunder diverse, unpredictable environmental conditions. The principalneurons at the right hand side of FIG. 4 are illustratively part of thecore network, and their outputs are applied to other portions of thecore network, although numerous other arrangements are possible.

Other examples of preprocessors that can be used in illustrativeembodiments include the following:

Sensor scaling. Neural network algorithms receiving sensor-array dataimplicitly assume that each sensor is weighted equally. Heterogeneoussensors or differently-scaled input sources violate this assumption andwill lead to impaired network performance. This compensatorypreprocessor algorithm rescales diverse sensors such that all inputs tothe SNN are statistically similarly scaled. This can be achievedmanually if different sensor input ranges are known (e.g., 5V sensorsmixed with 1.8V sensors), or inferred based on training set data. Sensorscaling also improves performance when a substantial fraction ofdeployed sensors are not particularly sensitive to any features of thedataset being analyzed, which typically occurs when the samplingstrategy is to deploy a great diversity of sensors without establishedresponsivity to the signals of interest.

Non-topographical contrast enhancement (NTCE). This is also referred toas high-dimensional contrast enhancement. This preprocessor algorithmapplies an adjustable high-dimensional sharpening filter onto raw inputpatterns for purposes of contrast enhancement.

Unsupervised global normalization. This preprocessor algorithmdecrements the activity of all individual sensor inputs based on theirmean, or widely projects all-to-all inhibition across sensor inputs, soas to limit the total input activation of the network to a narrow rangewithout disrupting the relational pattern of amplitudes across sensorsthat is the basis for signal specificity. Generally, globalnormalization should be applied after sensor scaling if thatpreprocessor is also used. This algorithm also underlies concentrationtolerance (also referred to as concentration invariance)—the concomitantability to recognize the same signal across a range of intensities evenwithout explicit training on the full range of intensities tested.

Mirror encoding. A related problem arises when multiple patterns(classification groups) are to be learned by an SNN, but one or more ofthese classification groups comprise substantially larger mean activityacross sensors than others. This can lead to an imbalance in networktraining and a prevalence of one-sided classification errors. Theprocess of mirror encoding generates a negative duplicate of eachsensory input (doubling their number), then offsets and scales theresulting values if necessary.

Ordinal forcing. Some versions of the Sapinet algorithm allow thenetwork to determine the population of interneurons that is madeavailable for differentiation during training (rather than allocatingseparate populations explicitly). While this flexibility improvesgeneralization performance, it renders the network sensitive to thestatistical distribution of input amplitudes, with broader, flatterdistributions systematically recruiting more interneurons. To addressthis problem, input levels are ranked and then assigned values drawnfrom a standard distribution as determined by their rank. This forcesthe input vector to conform to a single, optimized amplitudedistribution. This strategy is fast and effective, though it losessubstantial signal information; consequently, it is presently usedmainly for testing purposes. It has been largely superseded byheterogeneous duplication.

Several extensions and/or variants of Sapinet have been developed, asdescribed in more detail elsewhere herein.

Neuronal and synaptic heterogeneities. The ability to leverageheterogeneity has long been recognized in neuromorphic systems.Heterogeneities in the properties of principal neurons, interneurons,and their synapses in Sapinet variants improve statisticalregularization, generalization properties, and classificationperformance, expanding the capacity of the network to perform well underdiverse, unpredictable environmental conditions. These heterogeneitiesinclude the heterogeneous duplication preprocessor described above, butalso include heterogeneities in interneuron and principal neuron spikingthresholds, in the maximum synaptic weights that determine the feedbackinterneuron receptive field order k, in synaptic learning rates, inconvergence and projection ratios, and in other cellular and synapticproperties, often specific to particular network layers. Each of theseheterogeneities can provide improvements to network performance underparticular circumstances.

Neuromodulation. Neuromodulation broadly describes a constellation ofinterdependent state changes across a network that can dynamicallyreconfigure it for different purposes. An additional, novel extension tothe neuromodulation concept in Sapinet is to implement neuromodulationas a trajectory across state configurations (neuromodulatory sweep),such that the results of the best available state configuration can beapplied to the current input stream without the need to introspectivelyassess which configuration to apply. We have shown this to improveclassification performance under very high noise (FIG. 8(c)). Second,neuromodulation also can be used to regulate the stringency of thenon-topographical contrast enhancement preprocessor, in either a staticor trajectory form. Third, neuromodulation within the inference networkcan be deployed to regulate the learning versus recall states, as hasbeen proposed for the biological piriform cortex. In concert with otherinference network properties, this function can improve “learning in thewild” performance by dynamically shifting between learning and recallmodes without supervision (e.g., using an inference network). Morebroadly, Sapinet will broadly deploy the concept of transitioningthrough orderly sequences of interdependent parameter states in order toincrease the performance and adaptability of the network.

Adaptive network expansion (ANE). Sapinet intrinsically excels at onlinelearning—the ability to acquire new class memories without losingexisting memories or requiring careful retraining protocols. Itsextension, lifelong learning, describes the highly desirable propertywherein these new class memories can be acquired indefinitely. Sapinetachieves online learning in part through the permanent differentiationof feedback interneurons in the core network; this process takes thesedifferentiated interneurons out of the “trainable” population and hencelimits the learning capacity of an instantiated network as the trainableinterneuron population becomes depleted. However, Sapinet is able to addnew, differentiable interneurons to an existing, trained network withoutdisrupting the existing class memories (adult neurogenesis).Accordingly, new interneurons can be added indefinitely to replace thosethat have been differentiated out of the trainable pool, expanding thenetwork in proportion to the number of different class memories thathave been learned.

The strict allocation and replacement of interneurons described inconjunction with illustrative embodiments herein is straightforward andeffective, but a more complex algorithm for the allocation anddifferentiation of GC interneurons increases the capacity of Sapinet togeneralize among input patterns. This is referred to in the machinelearning literature as “learning beyond experience,” a potent form oftransfer learning. Specifically, a large undifferentiated population ofcore network interneurons is provided for any encountered stimulus todifferentiate. Distinct but similar input patterns therefore may share afraction of their responsive interneurons even after fulldifferentiation, thereby creating a basis for similarity. The challengeis to regulate the number of interneurons differentiated by any newrepresentation irrespective of its internal statistics. The statisticalregularization enabled by the heterogeneous duplication preprocessor,coupled with excitatory weight and interneuron thresholdheterogeneities, enables this variable to be managed (e.g., withheterogeneous duplication, as described above, replacing ordinalforcing).

Under this interneuron recruitment model, fully differentiatedinterneurons are then replaced post hoc by new, trainable interneuronsvia ANE in order to enable lifelong learning. It should be noted thatsuch references to replacement of differentiated interneurons herein donot imply that the differentiated interneurons are removed from thenetwork. Instead, both the differentiated interneurons and the newinterneurons now are embedded within the expanded network. ANE increasescoding efficiency and reduces memory interference by allocatinginterneurons preferentially where they are most needed, and/or pursuantto the learning of specific fine discriminations between very similarsensor inputs (supervised perceptual learning). ANE can also be appliedto certain preprocessors (e.g., to the inhibitory interneurons utilizedby the non-topographical contrast enhancement and global normalizationpreprocessors) and to certain instantiations of the inference network(e.g., to support supervised perceptual learning), as illustrated inFIG. 2.

The inference network 211 illustratively has multiple levels ofcomplexity that can encompass several distinct functions in the completeSapinet network.

A simple effect of an inference network is “contextual priming,” inwhich the priming of the interneuron population in the core feedbacknetwork enhances classification performance (e.g., FIG. 8(d)). Thispriming effect also can enable the sequential recognition of multipleknown signals that may be simultaneously present, rather than forcingthe network toward only a single conclusion. Contextual priming can alsobe deployed as part of a stimulus, to enable the correct parsing of asituation where the same signal should be classified differentlydepending on other situational factors that are not part of the signal.This priming signal of course can be determined based on a sensor orequivalent input, but this mechanism (deploying the priming signal ontointerneurons) is a more powerful method of achieving such an outcomecompared with communicating this contextual signal via additionalstandard sensor inputs.

A slightly more complex version of the inference network conductsassociative memory-like pattern completion operations, participating inthe gamma cycle in parallel with the direct principal neuron—interneuronfeedback loop and serving in part to counteract negative noise (FIG. 2).This form of inference network can increase the performance andflexibility of a Sapinet network, incorporating two memory systemswithin a single recurrent attractor network. It also is capable of the“neuromodulatory” regulation of learning vs. recall, as discussed above,enabling Sapinet to, for example, turn on learning whenever a stimuluswas not recognized (i.e., a “none of the above” outcome). Finally, in a“hypothesis testing” mode, this network also can drive priming effectsso as to facilitate the recognition of multiple knowns within a singlesample.

A more sophisticated implementation of the inference networkincorporates and enriches each of the above capabilities within amanifold learning context. Briefly, by constructing the moresophisticated, lifelong-learning version of the core feedback networkdescribed above, similarity can be more richly and specificallyrepresented, and repeated sensory experiences then can be used to buildexplicit manifolds within the inference network to define class memories(e.g., via stacked sparse manifold transforms). Among other potentialadvantages, this process enables two qualitatively new capacities to bedeveloped: supervised perceptual learning and hierarchicalclassification. Hierarchical classification enables classificationmodels to be built where additional precision can be gained underfavorable circumstances. A class of “orange” odors hence can besubdivided into “Valencia orange,” “tangerine,” and “clementine” (basedon sufficient differential training). If a signal is not clean enough toidentify with the desired certainty which of these three classes itfalls into, it can be identified with greater certainty as the nextbroader hierarchical class (equivalence class; here corresponding to“orange”). In the absence of such hierarchy, training on these threefiner-scale classes impairs the capacity to recognize the broader class.Supervised perceptual learning, in turn, enables the network to learn tomore strongly differentiate two physically similar signals by learningto emphasize their reliable differences and elide their similarities byadjusting the allocation of inhibition. Essentially, relatively reliablesub-patterns are deployed in the same manner as the full patterns inorder to remap similarity relationships in service to their relativeimplications rather than strictly to their physical natures.

In these ways, manifold learning enables full instantiation of asimilarity-based hierarchical learning scheme, in which poor-qualitysignals (with substantial noise and inter-sample random differences) canbe accurately identified as members of the broadest equivalence group ofthe class memory, whereas higher-quality, lower-noise signals canadditionally be sub-classified within finer-scale equivalence groupswithin the hierarchical representation. That is, after training, “wine”could be identified under very high background interference, whereas awell-trained Sapinet could, under low-noise circumstances, distinguish“Merlot” from “Malbec.” Like the mammalian olfactory system, this wouldof course require prior training to learn to differentiate the twovarieties. In both cases, the primary limitation on classificationprecision (as opposed to accuracy) is the richness of training, and thesecondary limitation is sampling error (noise).

A number of example use cases of illustrative embodiments will now bedescribed in more detail. These example use cases may be viewed ascarrying out particular automated actions using outputs generated bySapinet.

Sapinet is applicable to any problem based on the learning andclassification of sensory input populations that do not exhibit relevantlow-dimensional structure, such as the two-dimensional patterns of avisual image. This is likely to render Sapinet non-competitive in visualclassification problems such as ImageNet and MNIST. However, a widevariety of applications are effectively addressed by Sapinet. It shouldbe noted that, even beyond the algorithmic relevance of Sapinet, theexistence of energy-efficient neuromorphic hardware such as the IntelLoihi means that functional embedded devices based on the Sapinetalgorithms are achievable in the near term. Advantageously, Sapinet canbe used with arbitrary sensor arrays of any sort, enabling an end useror applications developer to select sets of sensors that best matchcustomer requirements. Sapinet can run on a variety of different typesof processing platforms, including by way of example, generic GPUhardware and on the Intel Loihi platform. Some examples of Sapinetapplications include:

1. Air quality monitoring, fire detection. Ongoing air qualitymonitoring is increasingly important in factories, mines, officebuildings, laboratories, HVAC systems, and other environments includinghomes and schools. Sapinet-based embedded devices can be standalone ornetworked devices, configured, for example, to report the presence ofspecific detected contaminants along with estimates of certainty.

2. Chemical waste identification, chemosensory landmine detection, acutedisaster site chemical monitoring. Handheld devices with embeddedneuromorphic hardware and arbitrary sensor arrays can be carried intochallenging conditions and deployed to quickly identify airborne ordissolved chemicals (depending on the sensor arrays utilized). Sensorpoisoning and time- or exposure-based sensor decay and drift can becompensated for in the field by rapid retraining with standards.Similarly, replacement sensors can be quickly calibrated in the field inthe same way.

3. Chemical species leak detection. Chemical species sensor systems forleak detection are of specific interest to NASA and other industries.

4. Spectral signature identification. Hyperspectral cameras deployed bysurveillance drones and aircraft produce single-pixel spectralsignatures. These spectra, discretized into defined bands, arediagnostic for features of interest and are well matched to Sapinet'sstrengths. Because these signals vary in time, this is an applicationthat would make use of the ongoing sampling mode of the Sapinet thetacycle.

5. Medical diagnostic dataset assessment. Diagnostic datasets includearbitrary lists of measurements at arbitrary scales; patterns amongthese measurements are diagnostic for clinical status. For example, theWisconsin Breast Cancer dataset includes several measurements of cellnuclei: their areas, their radii, their perimeters, and definitions oftexture, concavity, and fractal dimension, among others. These valueseach have different units and vastly different ranges of magnitude. Withthe appropriate preprocessors, these numbers can be used directly totrain Sapinet and then to classify additional samples for malignancywith high fidelity.

6. Microarray and other gene or protein expression signatures.Applications include cancer diagnostics, risk factor assessment forgenetic conditions, and many other biomedical assessments; at present, awide variety of analysis techniques are being assessed and compared withone another for diagnostic reliability. Microarray signatures compriselarge sets of sensor values (i.e., high-dimensional patterns) withoutinternal low-dimensional structure, and hence are well matched toSapinet's strengths. Moreover, very high-dimensional patterns, which arecomputationally intensive to assess on hardware that is not highlyparallel, can be analyzed very quickly with Sapinet on appropriateneuromorphic hardware (FIG. 10(b)).

It is to be appreciated that the particular use cases described aboveare examples only, intended to demonstrate utility of illustrativeembodiments, and should not be viewed as limiting in any way. Automatedactions taken based on outputs generated by a neuromorphic algorithm ofthe type disclosed herein can include particular actions involvinginteraction between a processing platform implementing the neuromorphicalgorithm and other related equipment utilized in one or more of the usecases described above. For example, outputs generated by a neuromorphicalgorithm can control one or more components of a related system. Insome embodiments, the neuromorphic algorithm and the related equipmentare implemented on the same processing platform, which may comprise acomputer, mobile telephone, handheld sensor device or other type ofprocessing device.

These and other Sapinet implementations are illustratively configured toachieve the rapid—even one-shot—learning of multiple arbitrary signalsin sequence and the subsequent detection of any of these signals underhigh levels of interference, even when the distribution of thatinterference is wholly unpredictable.

Conventional techniques generally depend on substantial amounts oftraining (hundreds or thousands of training trials, occupying many hoursper sample). Moreover, this training in conventional implementationstypically needs to encompass the actual variability in sample qualitythat will be encountered during testing. Such conventional approachestherefore need to know what that variability is, and this becomes aproblem in environments where the background statistics may differ fromthose present under training conditions. Finally, in these conventionalapproaches, all of the samples that one might want to detect anddiscriminate are trained at the same time; in order to add a new samplelater, network training is started over from scratch.

Sapinet embodiments disclosed herein advantageously overcome these andother drawbacks of conventional practice, through implementation offeatures and functionality that illustratively include one or more ofthe following.

1. The generation in the core network via learning of a heterogeneouspopulation of permanently differentiated interneurons that respond toincreasingly higher-order diagnostic features of a trained signal.

2. The implementation of in the core network ANE to enable lifelonglearning. This illustratively refers to the addition of new, naïveneurons to replace those that are permanently differentiated bylearning. This enables “lifelong learning” by supplying enough newneurons to enable the subsequent learning of an indefinite number of newsignals. Sapinet is particularly configured to facilitate such lifelonglearning.

3. Preprocessing using heterogeneous duplication. This preprocessingtechnique reduces the statistical variability of diverse input signalswithout significantly reducing their distinguishing features. With apreprocessor of this type, the network can be deployed into increasinglyunpredictable environments and process a broader range of inputs withhigh fidelity.

4. The implementation of a neuromodulatory sweep, using a dynamicaltrajectory of changing states in particular network elements toessentially re-compute network output over a range of different networkproperties and then choose the best one.

5. The implementation of an inference network. This network inillustrative embodiments is highly heterogeneous; it constitutesmultiple central computations that improve performance. For example, theinference network inserts illustratively itself into the core network'sfeedback loop, further biasing the network into particular attractor(s)by extracting and/or providing additional information. This informationcan arise from richer learned representations (e.g., manifold learningfor hierarchical classification, as described elsewhere herein), or fromprior information derived from other (multimodal) networks (for example,on a robot, visual information might provide some cues as to whichchemical cues are more likely, and the inference network can insertthese priors into the core network to make a correct result that muchmore likely even when it is really difficult). Such embodimentsintegrate various types of rich information into the core network, byhaving the inference network also learn about the permanentlydifferentiated interneurons and be able to associate these witharbitrary external sources of information. Its eventual effect is tobias some proportion of the “correct” interneurons to improveperformance (e.g., as illustrated in FIG. 8(d)).

6. Many of the above techniques rely on a core principle of structuredheterogeneity—that is, use a population of slightly different elements(or different states over time) to represent information in adistributed form, and use this distributed information to maximizeperformance.

7. Configuration of an SNN to use the phase (fine scale timing) ofspikes within gamma oscillations as an information metric, and/or toself-modify a representation via feedback to learn and follow anattractor.

These particular features and functionality of illustrative embodimentsare presented by way of example only, and should not be considered aslimiting in any way.

These and other features and functionality in some embodiments achieveonline learning and lifelong learning capabilities by, for example,implementing a gamma feedback loop for iterative denoising and odoridentification, and using the specific phase (timing) of spikes withingamma as an information metric.

In some embodiments, Sapinet provides what is referred to herein as“learning in the wild,” a term highlighting that such embodiments aredeployable in diverse environments with unknown stimuli without needingto tune the network specifically for these environments. Such a propertyis particularly important in the context of practical embedded devices.

Additional features and functionalities of some Sapinet embodimentsinclude the following.

1. “Online learning” is a term meaning that a network can keep learningnew things without disrupting prior learning (“catastrophicforgetting”). For example, Sapinet can learn a few signals, work toclassify noisy signals for a while, and then be trained on one or morenew signals that will simply add to that network's “library” of trainedsignals without disrupting the old ones or impairing its performance. Ingeneral, deep networks cannot do this; the new training not only takes along time but disrupts the older training weights.

2. “Lifelong learning” is a central unsolved problem that is, forexample, the focus of a major program at DARPA and elsewhere. Sapinetinstantiates clear, effective lifelong learning, illustratively by thedeployment of new interneurons into the network via ANE to replace thosethat have become dedicated, via learning, to recognizing a particularsignal or group of signals. Again, such replacement does not imply thatthe dedicated interneurons are removed from the network. The networktherefore gradually adds neurons over time, if and when new learning isperformed.

3. One-shot (or few-shot) learning simply refers to the fact that thenetwork can learn a representation effectively after only one (a few)training exposure(s), where one sample is processed over several gammacycles.

4. “Learning in the wild” is our term for a set of properties (includingproperties based on preprocessor capabilities) that enable Sapinetnetworks to be deployable in diverse environments with many unknowns,without needing to tune the network specifically for these environments,as described previously.

In some embodiments, the core network is configured to allow Sapinet torapidly learn input patterns (particular odors or other particularsignals) and to identify them in the presence of powerful interference.The input pattern is presented to an array of principal neurons. Everyindividual sensor activates one (or, in variants, more than one) ofthese principal neurons. The pattern of activity across these sensors isdiagnostic for a given odor/signal, but can easily be disrupted byinterference.

The core network in some embodiments is continuously driven by twooscillatory frequencies; the slower one governs sampling whereas thefaster one (“gamma”) governs processing. The faster oscillations areembedded within the slower one; in some embodiments, there is aparticular number of gamma cycles (e.g., five gamma cycles) embeddedwithin one sampling cycle (though this ratio can vary).

Principal neurons each generate zero or one “spike” (activity pulses)per gamma cycle. Strongly activated principal neurons evoke their spikesearlier in the gamma cycle, moderately weakly activated principalneurons evoke spikes later in the gamma cycle, and very weakly activatedprincipal neurons do not evoke a spike. This spike timing-dependentpattern of activity across these sensors directly reflects the rawactivation levels of sensors, and hence also is diagnostic for a givenodor/signal, but also can easily be disrupted by interference.

There also is a large population of interneurons. Principal neurons areeach connected to a random subset of these interneurons (say, 20%,though this can vary) and excite them. Interneurons in turn arespecifically assigned to deliver inhibition to the principal neuronsassociated with one given sensor (this rule can be varied, but therewill typically be some specificity). This inhibition will cause delaysin principal neuron spike times.

During training, relatively clean (low-noise) signals are used to trainthe network. Spiking activity in principal neurons activatesinterneurons. The interneurons have one or more embedded learning rules,illustratively implemented as one or more spike timing-dependentplasticity (STDP) rules, that cause them to be activated only bysufficient numbers of inputs from different principal neurons. When agiven interneuron is activated, the one or more STDP rules (over thecourse of a few gamma cycles) adjust the synaptic weights of thestarting inputs so that that interneuron now is only activatable by thatspecific set of k principal neuron inputs. This process is termed thedifferentiation of an interneuron, and it is irreversible. Some numberof interneurons is now selective for some higher-order diagnosticfeature of that odor/signal input. Important network variants includethose in which the interneurons are heterogeneous such that someinterneurons have relatively low values of k (e.g., they will beactivated by the coactivation of, say, three specific principal neurons)and others have high k values (e.g., will only be activated by thecoactivation of, say, fifteen specific principal neurons). An importantprinciple here is that interneurons learn to become activated only by(somewhat to highly) specific and diagnostic features of learnedodors/signals, and this learning is permanent. This process uses upinterneurons every time a new odor/signal is learned. This is addressedin illustrative embodiments through the implementation of ANEfunctionality—the addition of new “naïve” interneurons with (forexample) 20% random connectivity—so that new odors can be learned.

These activated interneurons then inhibit the principal neurons to whichthey are assigned. During training, the inhibitory synapses willprogressively alter their efficacies so as to form attractors to thetrained examples. In one illustrative embodiment, for example, aninhibitory synapse will learn to match the activity of its targetprincipal neuron so that it releases that principal neuron frominhibition just at the time when the principal neuron spikes—guidingthat neuron to do what it would do anyway under low-noise conditions.There are variants to the specific details of this rule.

During testing, odor/signal patterns may be disrupted by presentationvariabilities (concentration differences, plume dynamics, etc.) or byocclusion (other background odors/signals add to or subtract from theactivation of particular sensors, disrupting the pattern unpredictably).An important mechanism of Sapinet is that any diagnostic features thatremain detectable in that disrupted signal will activate theircorresponding interneurons (initially the lower-k interneurons). Thesewill deploy the “correct” inhibition onto principal neurons, affectingtheir spike timing such that the principal neurons more accuratelyreflect the odor/signal that is associated with those interneurons. Thiscauses the principal neuron activity in the second gamma cycle to be alittle bit closer to the memory of the learned odor/signal. The processthen iterates, and starts recruiting higher-k interneurons as theactivity pattern on each gamma cycle becomes closer to the learnedodor/signal. After a number of gamma cycles, the principal neuronactivity will converge onto a clear pattern that substantially matchesone of the learned patterns.

If the signal does not converge, then either the pattern was toooccluded to be recognized or the odor/signal presented was not one ofthose that had been learned. In either case, the network illustrativelyreturns an answer of “none of the above.” (This would be a correctresult in the latter case, or a Type II error in the former case).

The initial presentation of an occluded test sample may well recruitlower-k interneurons from more than one learned representation. This isnormal. As the gamma cycles iterate, the evolving representation will bedrawn towards one or the other as the higher-k interneurons arerecruited (because as k increases, the probability of multiple high-kinterneurons from different learned representations being responsive tothe same input pattern systematically decreases).

That is, Sapinet learns representations during training that areembedded in the pattern of synaptic weights to and from a heterogeneouspopulation of newly differentiated interneurons. These interneuronsremain in the network permanently and generate an attractor in thenetwork that pulls any representation toward it that shares some of itshigher-order diagnostic features. If multiple attractors initiallyattract a given representation, one will eventually win as the higher-kdiagnostic features are progressively included.

Multiple odors/signals can be learned in sequence, each forming its ownattractor in the network. (Odors/signals during training are labelled,so that a repeatedly presented odor can be used to modify its existingattractor rather than creating a separate attractor). Generally,learning a new odor/signal will be followed by the addition of newneurons via ANE—adding in new naïve interneurons to replace those thatwere differentiated by prior learning—so that new odors/signals can belearned with maximal effectiveness. This learning of new odors/signalscan go on at any time without disrupting prior learning, and can inprinciple continue indefinitely (“lifelong learning”).

Because inputs are expected to be higher-dimensional (i.e., a reasonablylarge number of sensors are deployed), these attractors can be keptsubstantially apart from one another. If very large numbers ofodors/signals are to be learned, the dimensionality (number of differentsensors) can be made correspondingly higher to maintain performance.

Accordingly, the Sapinet core network in illustrative embodiments isconfigured for generation via learning of a heterogeneous population ofpermanently differentiated interneurons that respond to increasinglyhigher-order diagnostic features of a trained signal. When a noisysignal is presented, some number of the lower-k diagnostic features arestill likely to be present, and their activation of interneurons willnudge the noisy signal closer to one or more of the trained signals. Asthis signal gets iteratively de-noised by this process, higher-kdiagnostic features will become present, and will increasingly serve todraw the signal towards just one of the learned representations. Thepermanent differentiation of interneurons also enables their efficientreplacement so that the network remains ready to learn any new arbitrarysignals that might be presented to it.

As indicated previously, Sapinet performance can be improved via theaddition of preprocessors, an expanded inference network,neuromodulation, and/or other features, as disclosed in conjunction withillustrative embodiments herein.

With regard to preprocessors, an important problem in real-worlddeployments is the unpredictability of the environment. Sensors responddifferently based on temperature, humidity, air quality, wear and tearover time, accumulated damage, and other factors. Conventionaltraining-based systems, such as deep networks, have vulnerabilities tocertain changes in the statistical distribution of inputs (see, e.g.,the substantial literature on “adversarial examples,” which disrupt deepnetwork performance using examples that usually appear easilyclassifiable to humans). Highly similar odor/signal patterns that havedifferent meanings can be difficult to separate reliably (because theirlearned representations will share even higher-k differentiatedinterneurons in common). The capacity of the Sapinet core network toeffectively deal with these realistic problems can be substantiallyenhanced by its series of preprocessors. For example, preprocessors asdisclosed herein are illustratively configured to provide enhancedperformance through heterogeneous duplication.

Heterogeneous duplication serves to regularize the distribution of inputlevels across the sensor array. Simple normalization corrects forpotentially large differences in absolute activity across the array,such that if you plotted the activation levels of sensors (Y axis)against a list of all sensors arranged in declining order of activation(X axis) the area under these curves could be made essentially constant.However, this still permits some inputs to yield broader/flatter versustaller/narrower distributions, and these can have different enougheffects on interneuron activation patterns that the network cannot bewell optimized for both. Heterogeneous duplication takes thesedistributions and regularizes them so that they all assume a more commondistribution.

In some embodiments, a heterogeneous duplication method is configuredsuch that, instead of each sensor directly feeding into a principalneuron (after preprocessing), each sensor feeds into one or moreexcitatory interneurons, and these in turn each feed into one or moreprincipal neurons. Hence, there will be multiple excitatory interneuronsand multiple principal neurons per sensor (“per column”), and each willhave slightly heterogeneous properties so as not to simply duplicate oneanother. Interestingly, this process leads to regularization among theactivity patterns of principal neurons (i.e., the distribution ofactivity levels follows a more predictable curve that enables the corenetwork that follows to be better optimized for a wider range of sensoryinputs, without having to tune the network for particular input types).In some embodiments, heterogeneous duplication allows the coefficient ofvariation (CV) to be reduced (or, equivalently, the coefficient ofdetermination (R²) to be increased) as the numbers of principal neurons(e.g., MCs) and excitatory feedforward interneurons (e.g., ET neurons)per sensor (column) increase. For a given number of principal neuronsper sensor/column, increasing the convergence ratio (the number ofexcitatory interneurons that converge onto each principal neuron) alsoreduces the coefficient of variation. Lower values of CV denote greaterconsistency, and in this context imply improved network performance. Insome embodiments, the mechanistic basis for this heterogeneousduplication effect illustratively involves an effect of drawing the rateof decay of sensor activation levels (across the principal neuronpopulation after sorting for activation amplitude) towards a decayfunction that is embedded in the degree and form of heterogeneity amongthe properties of the neurons.

Additional illustrative embodiments will now be described with referenceto FIGS. 5 through 10.

The embodiments to be described provide a neural algorithm for the rapidonline learning and identification of odorant samples under noise, basedon the architecture of the mammalian MOB and implemented on the IntelLoihi neuromorphic system. As with biological olfaction, the spiketiming-based algorithm utilizes distributed, event-driven computationsand rapid (one-shot) online learning. Spike timing-dependent plasticityrules operate iteratively over sequential gamma-frequency packets toconstruct odor representations from the activity of chemosensor arraysmounted in a wind tunnel. Learned odorants then are reliably identifieddespite strong destructive interference. Noise resistance is furtherenhanced by neuromodulation and contextual priming. Lifelong learningcapabilities are enabled by adult neurogenesis. The algorithm isapplicable to any signal identification problem in whichhigh-dimensional signals are embedded in unknown backgrounds.

Spike timing-based mechanisms of coding and computation operating withinplastic neural circuits present a central problem of interest to bothneuroscience and neuromorphic computing. We have found that acoordinated set of these mechanisms, hypothesized for the neuralcircuitry of the external plexiform layer (EPL) of the mammalian MOB,exhibits rapid learning of arbitrary high-dimensional neuralrepresentations and robust memory recall despite occlusion by randomsources of destructive interference. Based on these mechanisms, wederived a neural algorithm for the learning of odorant signals and theirrobust identification under noise, and instantiated it in the IntelLoihi neuromorphic system. The algorithm operates over a network ofexcitatory and inhibitory units that embed feedforward and recurrentfeedback circuit motifs. Information in the network is represented bysparse patterns of spike timing measured against an underlying networkrhythm. Learning is based on local spike timing-dependent plasticityrules, and memory is retrieved over sequential gamma-breadth packets ofspiking activity. The network can be effectively trained using one-shotlearning, and innately supports online learning; that is, additionaltraining on new stimuli does not disrupt prior learning.

While both biological and artificial olfaction systems recognizechemical analytes based on activity patterns across arrays of weaklyspecific chemosensors, mammalian olfaction demonstrates levels ofperformance in signal restoration and identification currently unmatchedby artificial systems. Indeed, the underlying identification problem isdeceptively difficult. Natural odors comprise mixtures of many differentodorant molecules; moreover, under natural conditions, different odorsfrom many separate sources intermingle freely and, when sampledtogether, chemically occlude one another in competition for primarychemosensor binding sites. This occlusion substantially disrupts theprimary sensory activation patterns that provide the basis for odorrecognition. Moreover, the patterns of potential occlusion are unrelatedto the input statistics of the odors of interest, and henceunpredictable. This presents an extraordinary signal restorationchallenge that has been recognized as one of the central problems inneuromorphic olfaction. By designing a neuromorphic algorithm based oncomputational principles extracted from the biological system, andimplementing it on a compact, field-deployable hardware platform, wesought to dramatically improve the performance and capabilities ofartificial chemosensory systems deployed into uncontrolled environments.

This biological system exhibits several important properties andmechanisms that we used to address the problem. Primary sensoryrepresentations of odor stimuli at steady state constitute intrinsicallyhigh-dimensional feature vectors, the dimensionality of which is definedby the number of receptor types (columns) expressed by the olfactorysystem; this number ranges from the hundreds to over 1000 in differentmammalian species. Each of these receptor types induces spiking in acorresponding group of principal neurons (e.g., MCs). Mechanistically,fast coherent oscillations in the gamma band (approximately 30-80 Hz),which are intrinsic to MOB circuitry, phase-restrict the timing of theseMC action potentials. This property discretizes spiking output intogamma-breadth packets, here enabling a robust within-packet phaseprecedence code^(17, 18) that disambiguates phase-leading fromphase-lagging spikes within the permissive epoch of each gamma cycle.Recurrent activity loops in MOB circuitry evince control systemsarchitecture, implementing gain control in the superficial layers andenabling autoassociative attractor dynamics in the deeper network. Odorlearning in the biological system is localized and rapid, and dependssubstantially on plastic synapses within the MOB, here instantiated asspike timing-dependent plasticity rules. The neuromodulatory tuning ofMOB circuit properties here is leveraged as an optimization trajectoryrather than a fixed state variable. Adult neurogenesis in the MOB, knownto be required for odor learning and memory, here provides indefinitecapacity for lifelong learning through the permanent differentiation andreplacement of plastic interneurons.

An example algorithm in the illustrative embodiments to be described isderived from these computational properties of the EPL neural circuit inthe biological MOB. We train and test the algorithm using data from theVergara et al. dataset, acquired from an array of 72 chemosensorsmounted across a wind tunnel, and show that it rapidly learns odorrepresentations and robustly identifies learned odors under high levelsof destructive interference, as well as in the presence of naturalvariance arising from odorant plume dynamics. The destructiveinterference model, impulse noise, is designed to model the effects ofintermixed, simultaneously sampled background odorants that effectivelyrandomize the activation levels of a substantial fraction of the primarysensors on which odor recognition depends. The algorithm exhibits onlinelearning and generalizes broadly beyond experience; accordingly, it canbe trained on relatively clean diagnostic samples using one- or few-shotlearning and then deployed into environments containing unknowncontaminants and other sources of interference.

FIG. 5A shows a portion 500 of an SNN utilized in implementing aneuromorphic algorithm in an illustrative embodiment. More particularly,FIG. 5A illustrates the architecture of the neuromorphic model. Sensorinput is delivered to the apical dendrite (AD) of each MC, which in turnexcites its corresponding soma (S). The resulting MC activation ispropagated out via its lateral dendrites to synaptically excite thedendrites of GCs. The distribution of excitatory connections (opencircles) is sparse and independent of spatial proximity. In contrast, GCspiking activity is delivered as inhibition onto its local, cocolumnarMC.

FIG. 5B shows an example of a processing device 510 implementing aneuromorphic algorithm using an SNN in an illustrative embodiment. Inthis embodiment, the processing device 510 comprises an Intel Loihineuromorphic chip having a multi-core network 512 that includes 64neuromorphic cores interconnected by a mesh of spike routers asillustrated. The neuromorphic cores (small squares) of the multi-corenetwork 512 operate in parallel and communicate through the mesh ofspike routers (circles). Also depicted are three embedded x86 Lakemontcores (LMT) 514 and four parallel input/output (IO) interfaces 516. TheLoihi neuromorphic chip illustrated in the figure is fabricated inIntel's 14 nm FinFET process and includes 2.07 billion transistors overthe many-core mesh. It is to be appreciated that use of the Intel Loihineuromorphic chip in illustrative embodiments herein is by way ofexample only, and the disclosed neuromorphic algorithms can beimplemented using a wide variety of alternative integrated circuits orother processing devices.

FIG. 5C illustrates odorant delivery from an odorant source 522 to a72-element chemosensor array 524 deployed within a wind tunnel 526. Ninebanks of eight sensors each were deployed across the full 1.2 m breadthof the wind tunnel 526. In this embodiment, presentation of acetone ortoluene to the chemosensor array 524 resulted in characteristic patternsof spiking activity across the 72 MCs. Stronger sensor activation led tocorrespondingly earlier MC spikes within each gamma cycle. In theabsence of noise, the response was odor-specific but stationary acrossfive sequential gamma cycles. Adjacent indices refer to sensors that arein adjacent locations across the wind tunnel, irrespective of theirtype. Inhibitory epochs were 20 timesteps (ts) in duration, as werepermissive epochs.

These and other aspects of the illustrative embodiments of FIGS. 5A, 5Band 5C are described in more detail below.

The structure of the model network of FIG. 5A based on the circuitry andcomputational properties of the mammalian MOB, is optimized forefficient implementation as an SNN on the Loihi chip shown in FIG. 5B.In particular, we instantiated some core principles of MOB computationthat we have hypothesized for the biological system, including (1) thedynamically acquired, learning-dependent topology of the lateralinhibitory network of the EPL, (2) the importance of gamma-discretizedspike timing-based computation in the EPL, (3) the principle that MCsdeliver excitation to GCs irrespective of distance, whereas GCseffectively inhibit MCs only locally, and only via GC spiking, (4) theprinciple that this inhibition of MCs by GCs predominantly manifests asdelays in MC spike times on the gamma timescale, (5) the principle thatthese fine-timescale EPL computations do not meaningfully influence thecoarse-timescale computations of the glomerular layer, (6) the principlethat only a minority of principal neurons participate in gamma dynamicsduring any given stimulus presentation, (7) the permanentdifferentiation of GCs by the process of odor learning, and theconsequent need for replacement by adult neurogenesis, and (8) theutility of treating neuromodulation as an optimization trajectory ratherthan as a stationary state.

Like the mammalian MOB, the neuromorphic EPL network is implicitlycolumnar, as illustrated in FIG. 5A. Each column comprises a single MCprincipal neuron as well as up to 50 inhibitory GC interneurons, coupledby moderately sparse intercolumnar excitatory synapses (connectionprobability=0.2) and local (intracolumnar) inhibitory synapses, althoughother arrangements can be used in other embodiments. We activated theMCs of a 72-column EPL network using the “Gas sensor arrays in opensampling settings” dataset published by Vergara et al. and availablefrom the UCI Machine Learning Repository. Samples were drawn from thechemosensor array 524 of 72 metal oxide gas sensor (MOS) elementsspatially distributed across the full 1.2 m breadth of the wind tunnel526, as illustrated in FIG. 5C. From the 180 second datastreamscomprising each odorant presentation in this dataset, sensor arrayresponses were sampled (“sniffed”) from a common point in time andpresented to the EPL network for training or testing. That is,individual odor samples (“sniffs”) comprised discrete feature vectors inwhich the pattern of amplitudes across vector elements reflected odorquality, as well as concentration-based variance owing to plume dynamicsin the wind tunnel.

The biological EPL network is intrinsically oscillogenic in the gammaband (30-80 Hz), and MC action potentials are statisticallyphase-constrained with respect to these local oscillations. In ouralgorithm, MC spikes were constrained in time by an ongoing networkoscillation with alternating permissive and inhibitory epochs reflectingthe periodic inhibition of the MOB gamma cycle. Sensory integration andMC spiking were enabled only during permissive epochs, whereasinhibitory epochs reset and held the activation of all MCs at zero.Therefore, in the absence of learning, and given stationary sensorinput, the temporal patterning of spikes evoked by a given odor directlyreflected sensor activation levels—stronger excitation evokedcorrespondingly earlier spikes—and was repeated across successive gammacycles. Different odors evoked correspondingly different spatiotemporalspike patterns across the MC population, thereby generating a hybridchannel/phase code, or precedence code, on the gamma timescale.

This dynamical architecture advantageously enables multiple iterativecycles of processing for each sample by taking advantage of thedifferences in timescale between sampling (4-8 Hz in rodent sniffing,100 Hz in the Vergara et al. dataset) and processing (30-80 Hz gammaoscillations in the rodent MOB, 100 kHz in the Loihi chip). In thepresent instantiation of the algorithm, five gamma cycles, eachrequiring 0.4 ms to execute, were embedded within each odor presentation(“sniff”) for both training and testing. After learning, GC feedbackinhibition on each successive gamma cycle iteratively modified MC spiketiming and hence altered the precedence code. Network output thus wasinterpreted as an evolving series of representations, in which eachdiscrete representation comprised a population of spikes, with eachspike defined by the identity of the active MC and the spike latencywithin the corresponding gamma cycle. These representations then wereclassified based on their similarities to each of the representationsknown by the network.

FIGS. 6A through 6C illustrate plasticity rules of a neuromorphicalgorithm in illustrative embodiments.

Referring initially to FIG. 6A, this diagram illustrates an excitatoryplasticity rule. During training, repeated coincident MC spikesconverging onto a given GC activated that GC, and developed strongexcitatory synaptic weights thereon, whereas other inputs to that GCwere weakened and ultimately eliminated. Excitatory plasticity renderedGCs selective to higher-order features of odor representations. Forexample, after training on toluene or acetone, a number of GCs becameresponsive to specific combinations of activated MCs.

FIG. 6B illustrates an inhibitory plasticity rule. During training, theweight (duration) of spike-mediated GC inhibition onto its cocolumnar MCincreased until the release of this inhibition coincided with spikeinitiation in the MC apical dendrite. The learned inhibitory weightcorresponded to a blocking period ΔB during which spike propagation inthe MC soma was suppressed.

Turning now to FIG. 6C, an illustration of the iterative denoising of anoccluded test sample is shown. Partially-correct representations in MCsevoke responses in some of the correct GCs, which deliver inhibitionthat draws MC ensemble activity iteratively closer to the learnedrepresentation. Three permissive epochs interspersed with two inhibitoryepochs are depicted. In the first permissive epoch, a partial overlapwith a learned representation is shown, along with noise. MCs spike inthe permissive phase of the gamma cycle and GCs spike in the inhibitoryphase of the gamma cycle. In the third permissive epoch, a recall of thelearned representation is shown.

These and other aspects of the illustrative embodiments of FIGS. 6A, 6Band 6C are described in more detail below.

Excitatory Plasticity Determines GC Receptive Fields

Each gamma-constrained array of MC action potentials, in addition toserving as network output, also drove its complement of postsynaptic GCsacross the network. During learning, the synaptic weights between MCsand GCs were systematically modified by experience. GCs were modeled assingle-compartment neurons that accumulated excitatory synaptic inputsfrom their widely distributed presynaptic MCs. Upon reaching threshold,they generated spike events that inhibited their cocolumnar postsynapticMC in the subsequent gamma cycle.

GC spiking also initiated excitatory synaptic plasticity. Specifically,GCs learned to respond to higher-order stimulus features by becomingselective for specific combinations of MC spiking activity. To do this,we implemented an STDP rule that learned these input combinations interms of a spike phase precedence coding metric on the gamma timescale.Under initial conditions, GCs required moderately synchronous spikeinputs from several presynaptic MCs in order to evoke an actionpotential. Classical STDP most powerfully strengthens the synapticweights of synapses mediating presynaptic spikes that immediatelyprecede a postsynaptic spike; we implemented this principle with aheterosynaptic additive STDP rule that strengthened these synapses andweakened all other incoming synapses, including those in which thepresynaptic MC spiked at other times or not at all (FIG. 6A).Accordingly, spiking GCs ultimately learned a fixed dependency on thesynchronous firing of a set of k MC inputs, with inputs from other MCsdecaying to zero (effectively a “k winners take all” learning rule).Consequently, at the end of the training period, the response to eachtrained odorant evoked a distributed ensemble of GCs tuned to adiversity of stimulus-specific higher-order correlation patterns.

Inhibitory Plasticity Denoises MC Representations

Spikes evoked by GC interneurons delivered synaptic inhibition onto theMC of their local column. As proposed for the biological system, theweights of GC-mediated inhibitory inputs regulated the timing of MCspikes within the permissive phase of the gamma cycle, with strongerweights imposing greater MC spike time delays within each gamma cycle.In the neuromorphic system, a GC spike blocked the generation of a spikeon its follower MC for a period of time corresponding to the inhibitorysynaptic weight. During odor learning, the durations of GC spike-evokedinhibitory windows were iteratively modified until the release ofinhibition on the MC soma coincided with a threshold crossing in the MCapical dendrite resulting from integrated sensory input (FIG. 6B).During testing, the end of the GC inhibitory window permitted the MC tofire, and evoked a rebound spike in the MC even in the absence ofsufficient apical dendritic input. Synaptic inputs from multiple localGCs onto a common MC were independent of one another, enabling a diverserange of higher-order GC receptive fields to independently affect theMC. During testing, occluded inputs activated some fraction of GCs,which then modified their postsynaptic MC spike times such that therepresentation in the next gamma cycle was closer to a learned odorant,hence activating an increased fraction of its corresponding GCs. Thisprocess continued iteratively until the learned representation wasrecalled (FIG. 6C).

This inhibitory plasticity rule enables the EPL network to learn thetiming relationships among MC spikes in response to a given odorstimulus. Consequently, because relative spike times signify MCactivation levels, the network effectively learns the specificratiometric pattern of activation levels among MCs that characterizes agiven odor. This spatiotemporal basis for odor representation enables asubstantially greater memory capacity than would be possible withspatial patterning alone; for example, two odors that activate the samepopulation of MCs, but at different relative levels, can readily bedistinguished by the trained network. Moreover, it consumes fewer spikesthan rate-coding metrics, and can be read out much more quickly becauseit does not need to integrate multiple spikes over time to estimaterate. Finally, this spike timing-based metric for relational encoding,coupled with odor-specific profiles of feedback inhibition, rendersthese memory states as attractors, enabling incoming stimuli to becorrectly classified by the trained network despite surprisingly highdegrees of destructive interference. The trained EPL network thuscomprises a spike-timing based autoassociator, embedding an arbitrarynumber of content-addressable memories.

FIG. 7 is a set of graphical plots (a) through (d) showing aspects ofodor learning in illustrative embodiments. In an initial simulation, anoccluded instance of toluene (impulse noise P=0.6) was presented to anuntrained network. The untrained network does not update the response tooccluded toluene over five gamma cycles. The same occluded instance oftoluene is then presented to a plastic network trained on (non-occluded)toluene. It was found that the activity profile evoked by the occludedsample was attracted to the learned toluene representation oversuccessive gamma cycles. Finally, the same occluded instance of toluenewas presented to a network trained on non-occluded toluene withexcitatory, but not inhibitory, plasticity enabled. The omission ofinhibitory plasticity rendered the network unable to denoise MCrepresentations during testing.

FIG. 7(a) shows the Jaccard similarity between the response to occludedtoluene and the learned representation of toluene systematicallyincreased over five gamma cycles in the trained network (panel b), butnot in the untrained network (panel a) or the network with inhibitoryplasticity disabled (panel c).

FIG. 7(b) illustrates that the Jaccard similarity increased reliablyover five gamma cycles when averaged over 100 independently generatedinstances of occluded toluene (impulse noise P=0.6). Error bars denotestandard deviation.

FIG. 7(c) shows that, during learning, the number of GCs tuned totoluene increased over the five successive gamma cycles of training.

FIG. 7(d) shows mean Jaccard similarity in the fifth gamma cycle as afunction of the number of undifferentiated GCs per column. Meansimilarity is averaged across 100 occluded instances of toluene (impulsenoise P=0.6); error bars denote standard deviation. Five GCs per columnwere utilized for all other simulations described herein.

These and other aspects of the illustrative embodiments of FIG. 7 aredescribed in more detail below.

Odor Learning Enables Identification of Occluded Stimuli

We first trained the 72-column network on the odorant toluene in oneshot (i.e., one sniff, enabling learning over five gamma cycles), andthen, with plasticity disabled, tested the response of the trainednetwork to presentations of toluene contaminated with destructiveinterference. To generate this interference, we entirely replaced aproportion P of the sensory inputs with random values (impulse noise,P=0.6 unless otherwise indicated) to represent strong and unpredictablereceptor occlusion through simultaneous activation or inhibition byother ambient odorants. The occluded inputs remained consistent over thefive gamma cycles of a sniff. In a naïve network, the presentation ofoccluded toluene yielded an essentially stationary and uninformativerepresentation (FIG. 7(a)). However, in the trained network, the spikingactivity generated by occluded toluene was attracted over the five gammacycles toward the previously learned toluene representation, enablingclear identification of the occluded unknown (FIGS. 7(a)-7(b)). Incontrast, if inhibitory plasticity (FIGS. 6B and 6C) was suppressedduring training, the trained EPL network was unable to denoise the MCrepresentation (FIG. 7(a)).

As hypothesized for the biological MOB, odor learning in the networkinduces the permanent differentiation of granule cells (FIG. 7(c)) thatthereby become selective for higher-order feature combinations that arerelatively diagnostic of the learned odor. We tested whether increasedallocations of GCs, enabling each MC to be inhibited by a broaderselection of feature combinations, would improve odor learning andidentification under noise. We found that increasing the number ofundifferentiated GCs per column improved the robustness of signalrestoration, increasing the similarity of the occluded signal to thelearned representation after five gamma cycles (FIG. 7(d)).Nevertheless, we limited our simulations to five GCs per trained odorantand five gamma cycles per sniff in order to avoid ceiling effects andthereby better reveal the variables of greatest interest.

These illustrative embodiments also illustrate that adult neurogenesisenables lifelong learning. The learning algorithm in the presentembodiments irreversibly consumes GCs. Each odor memory is associatedwith a distributed population of differentiated GCs tuned to its complexdiagnostic features. Fully differentiated, mature GCs do not undergofurther plasticity and hence are protected from catastrophicinterference. The learning of successively presented new odorants,however, would be increasingly handicapped by the declining pool ofundifferentiated GCs (FIG. 7(d)). The competition among distinct newodorants can be substantially reduced by sparser initial MC→GCconnectivity and higher numbers of GCs, among other parameters; however,genuine lifelong learning in such a system requires a steady source ofundifferentiated GCs. Exactly this resource is provided to the mammalianolfactory system by constitutive adult neurogenesis. The important roleof adult neurogenesis in odor learning is therefore interpreted in thislight, in some embodiments herein.

In the neuromorphic algorithm, constitutive adult neurogenesis wassimulated by configuring a new set of five GCs in every column aftereach successively learned odor stimulus. Hence, training a 72-columnnetwork on ten odors yielded a network with 3600 differentiated GCs. NewGCs each received initial synaptic connections from a randomly selected20% of the MCs across the network, and delivered inhibition onto theircocolumnar MC.

FIG. 8 is a set of graphical plots (a) through (d) showing aspects ofmulti-odor learning in illustrative embodiments. The network was trainedon ten odorants, including toluene, acetone, methane, ammonia andbenzene.

A representation generated by a sample of occluded toluene (P=0.6) wasprogressively drawn towards the learned representation of toluene andaway from the learned representations of acetone and the other eightodorants.

FIG. 8(a) shows the Jaccard similarity to toluene that was evoked by theoccluded-toluene stimulus increased over five successive gamma cyclesuntil the stimulus was classified as toluene (similarity >0.8). Forclarity, only the above-noted five odorants are depicted.

FIG. 8(b) shows that the number of toluene-tuned GCs activated by theoccluded-toluene stimulus progressively increased over five gamma cyclesas the MC spiking activity pattern was attracted towards the learnedtoluene representation. GCs tuned to the other nine odorants werenegligibly recruited by the evolving stimulus representation.

Additional simulations measured network activity evoked by presentationof occluded instances of each of the ten learned odors followingone-shot learning. It was found that the same network can reliablyrecognize all ten odorants from substantially occluded examples (P=0.6).

FIG. 8(c) shows mean classification performance across all ten odorantsunder increasing levels of sensory occlusion (100 impulse noiseinstantiations per odorant per noise level). The abscissa denotes thelevel of impulse noise, that is, the proportion of MC inputs for whichthe sensory activation level was replaced with a random value. Thisfigure shows the proportion of correct classifications by an untrainednetwork, the proportion of correct classifications by a network trainedon all ten odorants, and the proportion of correct classifications by atrained network with the aid of a neuromodulation-dependent dynamicstate trajectory.

FIG. 8(d) illustrates the effects of GC priming on classificationperformance under extreme occlusion. One hundred independently generatedsamples of occluded toluene with impulse noise P=0.9 were presented tothe fully-trained network. The putative effects of priming arising frompiriform cortical projections onto bulbar GCs were modeled by loweringthe spike thresholds of a fraction of toluene-tuned GCs. As the fractionof toluene-tuned GCs so activated was increased, classificationperformance increased from near zero to over 80% correct.

These and other aspects of the illustrative embodiments of FIG. 8 aredescribed in more detail below.

Online Learning of Multiple Representations

We then trained the 72-column network sequentially with all ten odorantsin the dataset, using a one-shot training regimen for each odor. In eachcase, the network was trained on one odor first, followed by a secondodor, then by a third, until all ten odors had been learned. Similarresults were obtained irrespective of the order in which the tenodorants were trained. A set of new, undifferentiated GCs was added tothe network after each odor was learned, reflecting the effects of adultneurogenesis. It should be noted that subsequent odor training did notdisrupt the memories of previously learned odors; that is, the EPLnetwork supports robust online learning, and is resistant tocatastrophic forgetting. This capacity for online learning is importantfor memory formation under natural conditions, as well as for continuousdevice operation in the field; in either case, new signals of potentialsignificance may be encountered at unpredictable times, and incorporatednondestructively into an existing knowledge base.

We then tested the algorithm's capacity to recognize and classifyodorant samples that were strongly occluded by impulse noise, reflectingthe effects of any number of independent odorous contaminants that couldmask the odor of interest in uncontrolled environments. Followingtraining on all ten odorants, sensor-evoked activity patterns generatedby strongly occluded odor stimuli (impulse noise P=0.6) were attractedspecifically towards the learned representation of the correspondingodor. Notably, the same network was able to rapidly identify occludedinstances of all ten odors within five gamma cycles. An odor wasconsidered identified when the spatiotemporal pattern of its evokedspiking activity exceeded a Jaccard similarity of 0.75 to one of thenetwork's learned representations. Performance on this dataset understandard conditions was strong up to sample occlusion levels of P=0.6,after which increased occlusion began to gradually impair classificationperformance (FIG. 8(c)).

Neuromodulation and Cortical Priming Improve Classification Performance

Neuromodulators like acetylcholine and noradrenaline generate powerfuleffects on stimulus representations and plasticity in multiple sensorysystems including olfaction. Traditionally, they are treated as statevariables that may sharpen representations, gate learning, or bias anetwork towards one source of input or another. We instead modeledneuromodulatory effects as a dynamic search trajectory. Specifically, asthe neuromodulator is released in response to active olfactoryinvestigation (sampling), the local concentration around effectorneurons and synapses rises over the course of successive sniffs,potentially enabling the most effective of the transient neuromodulatorystates along that trajectory to govern the outcome of the stimulusidentification process. We implemented a gradual reduction in the meanGC spiking threshold over the course of five sniffs of a corrupted odorsignal, reflecting a concomitant increase in neuromodulator efficacy,and used the greatest of the five similarity values measured in the lastgamma cycle within each sniff to classify the test odorant. It should benoted that, under very high noise conditions, each of the five“neuromodulatory” states performed best for some of the test odors andnoise instantiations, indicating that a trajectory across a range ofneuromodulatory states could yield superior classification performancecompared to any single state. Indeed, this strategy yielded asubstantial improvement in classification performance at very highlevels of impulse noise, approximately doubling classificationperformance at P=0.8 (FIG. 8(c)).

In the biological system, MOB activity patterns resembling those evokedby a specific odor can be evoked by contextual priming that ispredictive of the arrival of that odor. We implemented this as a primingeffect exerted by ascending piriform cortical neurons that synapticallyexcite GCs in the MOB, the mapping between which can be learneddynamically. Specifically, we presented the network with odor samples atan extreme level of destructive interference (P=0.9) that largelyprecluded correct classification under default conditions (FIG. 8(c)).When fractions of the population of GCs normally activated by thepresented odor were primed by lowering their spike thresholds,classification performance improved dramatically, to a degreecorresponding to the fraction of primed GCs (FIG. 8(d)). That is, even aweak prior expectation of an incoming odor stimulus suffices to draw anextremely occluded odor signal out of the noise and into the attractor.

FIG. 9 is a set of graphical plots (a) and (b) showing aspects of odorlearning with plume dynamics in illustrative embodiments.

In these simulations, ten sniffs of toluene were drawn fromrandomly-selected timepoints within the dataset to illustrate samplingvariance arising from plume dynamics. It was found that the same networkreliably recognized all ten odorants from plume-varying andsubstantially occluded examples (P=0.4).

FIG. 9(a) shows that the Jaccard similarity to toluene that was evokedby the occluded, plume-varying toluene stimulus increased over fivesuccessive gamma cycles until the stimulus was classified as toluene(similarity >0.8). For clarity, only five odorants are depicted.

FIG. 9(b) shows mean classification performance across all ten odorants,with plume dynamics, under increasing levels of sensory occlusion (100impulse noise instantiations per odorant per noise level). The abscissadenotes the level of impulse noise. The curve shows the proportion ofcorrect classifications by a network trained on all ten odorants.

These and other aspects of the illustrative embodiments of FIG. 9 aredescribed in more detail below.

Sample Variance Arising from Plume Dynamics

In addition to occlusion by competing odorants, odor samples can varybased on the dynamics of their plumes (FIG. 5C), which evolve over time.We therefore tested the algorithm's ability to recognize and classifysamples of each odorant that were drawn from the wind tunnel atdifferent points in time. Specifically, in this paradigm, repeatedsamples of the same odorant differed from one another based on evolvingodor plume dynamics, whereas samples of different odorants differed fromone another both in plume dynamics and in the distribution of analytesensitivities across the sensor array. Following one-shot training onall ten odors as described above, the spiking activity generated byodorant test samples was attracted over the five gamma cycles towardsthe corresponding learned representation. Notably, plume dynamics aloneconstituted a relatively minor source of variance compared to impulsenoise.

We then tested the network on samples incorporating both plume dynamicsand impulse noise (P=0.4). Following one-shot training on all ten odors,we sampled each odor across widely dispersed points in time, andcontaminated each sniff with an independent instantiation of impulsenoise. Spiking activity was again attracted over the five gamma cyclesof each sniff towards the correct learned representation (FIG. 9(a)).Classification performance across levels of impulse noise from P=0.0 toP=1.0 (FIG. 9(b)) indicated that the addition of plume-based variabilitymoderately reduced network performance (compare to FIG. 8(c)). Networkperformance was not affected by the introduction of noise correlationsover time.

FIG. 10 is a set of graphical plots (a) through (g) showing aspects ofperformance of a neuromorphic algorithm using an SNN in illustrativeembodiments.

FIG. 10(a) illustrates classification performance of the EPL network incomparison to four other signal processing techniques. Raw,classification of unprocessed sensor signals. MF, median filter. TVF,total variation filter. PCA, principal components analysis. DAE, aseven-layer deep autoencoder. EPL, the neuromorphic EPL model. Each ofthe 10 odorants was presented with 100 independent instantiations ofimpulse noise, yielding 1000 total test samples.

FIG. 10(b) shows that the performance of the DAE improved when it wasexplicitly trained to map a variety of occluded instances of each odorto a common representation. To achieve performance superior to theone-shot-trained EPL network, the DAE required 3000 occluded trainingsamples per odorant. In this figure, the abscissa is the number oftraining samples per odorant (s/o), and the ordinate is theclassification performance (%).

FIG. 10(c) illustrates online learning. After training naïve EPL and DAEnetworks with toluene, both recognized toluene with 100% accuracy. Afterthen training the same network with acetone, the DAE learned torecognize acetone with 100% accuracy, but was no longer able torecognize toluene (catastrophic forgetting). In contrast, the EPLnetwork retained the ability to recognize toluene after subsequenttraining on acetone.

FIG. 10(d) shows gradual loss of the toluene representation in the DAEduring subsequent training with acetone. The ordinate denotes thesimilarity of the toluene-evoked activity pattern to the originaltoluene representation as a function of the number of training epochsfor acetone. Values are the means of 100 test samples. The inset showssimilarity between the toluene-evoked activity pattern and the originaltoluene representation in the EPL network before training with acetone(left) and after the completion of acetone training (right).

FIG. 10(e) illustrates similarity between the toluene-evoked activitypattern and the original toluene representation as the EPL network issequentially trained on all 10 odorants of the dataset. Values are themeans of 100 test samples.

FIG. 10(f) illustrates that the execution time to solution is notsignificantly affected as the EPL network size is expanded, reflectingthe fine granularity of parallelism of the Loihi architecture. In thepresent implementation, one Loihi core corresponds to one MOB column.

FIG. 10(g) illustrates that the total energy consumed increases onlymodestly as the EPL network size is expanded.

These and other aspects of the illustrative embodiments of FIG. 10 aredescribed in more detail below.

Classification Performance of the Neuromorphic Model

To evaluate the performance of the EPL model, we compared itsclassification performance to the performance of multiple conventionalsignal processing techniques: a median filter (MF), a total variationfilter (TVF; both commonly used as impulse noise reduction filters),principal components analysis (PCA; a standard preprocessor used inmachine olfaction), and a seven-layer deep autoencoder (DAE).Specifically, following training, we averaged the classificationperformance of each method across 100 different occluded presentationsof each odor, with the occlusion level for each sample randomly anduniformly selected from the range P=[0.2, 0.8], for a total of 1000 testsamples. Incorrect classifications and failures to classify both werescored as failures.

The neuromorphic EPL substantially outperformed MF, TVF, and PCA. Tomodel “one-sample” learning on the DAE for comparison with one-shotlearning on the EPL network, we trained a DAE with one sample from eachof the ten odorants over 1000 training epochs per odorant, with theodorants intercalated in presentation. The EPL network substantiallyoutperformed the DAE under these conditions, in which the training setcontained no information about the distribution of error that wouldarise during testing owing to impulse noise (FIG. 10(a)). To improve DAEperformance, we then trained it with 500 to 7000 samples of each of theten odorants, with each sample independently occluded by impulse noiserandomly and uniformly selected from the range P=[0.2, 0.8]. Under thistraining regimen, the deep network required 3000 samples per odorant,including the attendant information regarding the distribution oftesting variance, to achieve the classification performance that the EPLmodel achieved with 1 sample per odorant. With further training, DAEperformance exceeded that of the EPL network (FIG. 10(b)). We thentested the online learning capacities of the two networks, in which thepresentations of different odorants during training were sequentialrather than uniformly interspersed. After training both networks torecognize toluene using the methods of FIG. 10(b), both the EPL and theDAE exhibited high classification performance. However, after subsequenttraining to recognize acetone, the DAE lost its ability to recognizetoluene, whereas the EPL network recognized both odors with highfidelity (FIGS. 10(c)-10(d)). Susceptibility to catastrophic forgettingis a well-established limitation of deep networks, though somecustomized networks recently have shown improvements in their online(continual) learning capabilities that reflect some of the strategies ofthe EPL network, such as the selective reduction of plasticity inwell-trained network elements.

These results indicate that the EPL network ultimately serves adifferent purpose than techniques that require intensive training withexplicit models of expected variance in order to achieve optimalperformance. The EPL network is competitive with these algorithmsoverall, but excels at rapid, online learning with the capacity togeneralize beyond experience in novel environments with unpredictablesources of variance. In contrast, the DAE evaluated here performs bestwhen it is trained to convergence on data drawn from the distribution ofexpected variance; under these conditions, its performance exceeds thatof the present EPL network. EPL network instantiations are therebylikely to be favored in embedded systems intended for deployment in thewild, where rapid training, energy-efficiency, robustness tounpredictable variance, and the ability to update training with newexemplars are at a premium.

The EPL algorithm, while derived directly from computational features ofthe mammalian olfactory system, essentially comprises a spiketiming-based variant of a Hopfield autoassociative network, exhibitingautoassociative attractor dynamics over sequential gamma-breadth packetsof spiking activity. Since their conception, Hopfield networks and theirvariants have been applied to a range of computational problems,including sparse coding, combinatorial optimization, path integration,and oculomotor control. Because these studies typically model neuralactivity as continuous-valued functions (approximating a spike rate),they have not overlapped significantly with contemporary researchinvestigating spike-timing-based mechanisms of neural coding andcomputation—mechanisms that are leveraged in contemporary neuromorphicsystems to achieve massive parallelism and unprecedented energyefficiency. The EPL algorithm combines insights from these two bodies ofwork, instantiating autoassociative attractor dynamics within a spiketiming framework. By doing so, it proposes novel functional roles forspike timing-dependent synaptic plasticity, packet-based neuralcommunications, active neuromodulation, and adult neurogenesis, allinstantiated within a scalable and energy-efficient neuromorphicplatform (FIG. 10(f)-10(g)).

Contemporary artificial olfaction research often emphasizes thedevelopment of sensors and sensor arrays. Associated work on theprocessing of electronic nose sensor data incorporates both establishedmachine learning algorithms and novel analytical approaches, as well asoptimizations for sensory sampling itself. The biological olfactorysystem has both inspired modifications of traditional analytical methodsand guided biomimetic approaches to signal identification in bothchemosensory and non-chemosensory datasets. In comparison to thesediverse approaches, illustrative embodiments disclosed hereinincorporate multiple innovations relating, for example, to the rapidlearning of the EPL network, its spike timing-based attractor dynamics,its performance on identifying strongly occluded signals, and itsfield-deployable Loihi implementation.

The illustrative embodiments described in conjunction with FIGS. 5through 10 demonstrate that a simplified network model, based on thearchitecture and dynamics of the mammalian MOB and instantiated in theLoihi neuromorphic system, can support rapid online learning andpowerful signal restoration of odor inputs that are strongly occluded bycontaminants. These results evince powerful computational features ofthe early olfactory network that, together with mechanistic models andexperimental data, present a coherent general framework forunderstanding mammalian olfaction as well as improving the performanceof artificial chemosensory systems. Moreover, this framework is equallyapplicable to other steady-state signal identification problems in whichhigher-dimensional patterns without meaningful lower-dimensionalinternal structure are embedded in highly interfering backgrounds.

Additional details regarding methods applied in testing of theillustrative embodiments will now be described.

Dataset and Odorant Sampling

Sensory input to the model was generated from the “Gas sensor arrays inopen sampling settings” dataset published by Vergara et al. andavailable from the UCI Machine Learning Repository. The datasetcomprises the responses of 72 metal-oxide based chemical sensorsdistributed across a wind tunnel. There are six different sensormounting locations in the tunnel, three different settings of thetunnel's wind speed and three different settings of the sensor array'sheater voltage. In the present embodiments, we consider the recordingsmade at sensor location “L4” (near the mid-point of the tunnel), withthe wind speed set to 0.21 m s′ and the heater voltage set to 500 V. Thetunnel itself was 1.2 m wide×0.4 m tall×2.5 m long, with the sensorsdeployed in nine modules, each with eight different sensors, distributedacross the full 1.2 m width of the tunnel at a location 1.18 m from theinlet (FIG. 5C). The nine modules were identical to one another. Tomaintain the generality of the algorithm rather than optimize it forthis particular dataset, we here sampled the 72 sensors naïvely, withoutin any way cross-referencing inputs from the nominally identical sensorsreplicated across the nine modules, or attempting to mitigate theplume-based variance across these sensors. The turbulent plume shown inFIG. 5C is illustrative only; distribution maps of local concentrationsin the plume, along with full details of the wind tunnel configuration,are provided in the publication first presenting the dataset.

Ten different odorants were delivered in the gas phase to the sensorarray: acetone, acetaldehyde, ammonia, butanol, ethylene, methane,methanol, carbon monoxide, benzene, and toluene. For every tunnelconfiguration, each of these odorants was presented 10-20 times, andeach presentation lasted for 180 seconds. In the present embodiments, weconsider one of these 180-second plumes (chosen at random) for eachodorant.

We discretized each sensor's range of possible responses into 16 levelsof activation, corresponding to 16 time bins of the permissive epoch ofeach gamma cycle. The discretized sensor values were composed into a72-dimensional sensor activity vector, which then was sparsened bysetting the smallest 50% of the values to zero. Accordingly, eachodorant sample (“sniff”) presented to the EPL network comprised adiscrete 72-element sensor vector drawn from a single point in time andpresented as steady state. The training set underpinning one-shotlearning was based on single-timepoint samples drawn from the 90 secondtimepoint in each of the 180 second long odorant presentations. Testsets for the impulse-noise-only studies (FIGS. 7-8) comprised these sametimepoints, each altered by 100 different instantiations of impulsenoise. For the plume-variance studies (FIG. 9), test samples for eachodorant were drawn from different time points in the corresponding plume(specifically, across the range 30-180 seconds after odorantpresentation, at 5 second intervals) and were presented to the networkboth with and without added impulse noise.

The MOB EPL model therefore was instantiated with 72 columns, such thateach column received afferent excitation proportional to the activationlevel of one sensor. Because we here present the network in its simplestform, we treated the 72 columns as independent inputs, without craftingthe algorithm to combine the responses of duplicate sensor types, toweight the centrally located sensors more strongly, or to perform anyother dataset-specific modifications that might improve performance.Each model MOB column comprised one principal neuron (e.g., an MC) andinitially five GC interneurons that were presynaptic to that MC (for atotal of 360 GCs across all columns), though the number of GCs percolumn rose as high as 50 in other examples of highly trained modelsdescribed herein. MCs projected axons globally across all columns andformed excitatory synapses onto GCs with a uniform probability of 0.2(20%). Each GC, in turn, synaptically inhibited the MC within its columnwith a probability of unity (100%). GCs did not inhibit MCs from othercolumns, though this constraint can be relaxed without affecting overallnetwork function. To reflect the mapping of the algorithm to thephysical layout of the Loihi chip, we consider an MC and its co-columnarGCs to be spatially local to one another. However, there is nocomputational basis for the physical locations of neurons in the model;an MOB column is simply “an MC plus those inputs that can affect itsactivity.”

Intrinsic Gamma and Theta Dynamics

In the biological system, the profile of spike times across MCs isproposed to reflect a phase precedence code with respect to the emergentgamma-band field potential oscillations generated in the olfactorysystem. Spike timing-based coding metrics are known to offerconsiderable speed and efficiency advantages; however, they requirecomputational infrastructure in the brain to realize these benefits.Fast oscillations in the local field potential are indicative of broadactivity coherence across a synaptically coordinated ensemble ofneurons, and thereby serve as temporal reference frames within whichspike times in these neurons can be regulated and decoded. Accordingly,these reference frames are important components of the biologicalsystem's computational capacities.

In the MOB, gamma oscillations emerge from interactions of thesubthreshold oscillations of MCs with the network dynamics of the EPL(PRING dynamics). For present purposes, the importance of theseoscillations was twofold: (1) MC spike phases with respect to thegamma-band oscillations serve as the model's most informative output,and (2) by considering each oscillation as embedding a distinct,interpretable representation, repeated oscillations enable the networkto iteratively approach a learned state based on stationary sensoryinput. Notably, in vivo, piriform cortical pyramidal neurons areselectively activated by convergent, synchronous MC spikes, andestablished neural learning rules are in principle capable of readingsuch a coincidence-based metric. Because MC spike times can be alteredon the gamma timescale by synaptic inhibition from GCs, and their spiketimes in turn alter the responsivity of GCs, these lateral inhibitoryinteractions can iteratively modify the information exported from theMOB. In the neuromorphic EPL, each MC periodically switched between twostates to establish the basic gamma oscillatory cycle. These two stateswere an active state in which the MC integrated sensory input andgenerated spikes (permissive epoch) and an inactive state in which theexcitation level of the MC was held at zero, preventing sensoryintegration and spike generation (inhibitory epoch). The effects of theplastic lateral inhibitory weights from GCs were applied on top of thistemporal framework. The correspondence with real time is arbitrary andhence is measured in timesteps (ts) directly; that said, as Loihioperates at about 100 kHz, each timestep corresponds to about 10 us. Inthe present implementation, the permissive epoch comprised 16 ts and theinhibitory epoch 24 ts, for a total of 40 ts per gamma cycle. Notably,the duration of the permissive epoch directly corresponds to the numberof discrete levels of sensory input that can be encoded by our spiketiming-based metric; it can be expanded arbitrarily at the cost ofgreater time and energy expenditures.

A second, slower, sampling cycle was used to regulate odor sampling.This cycle is analogous to theta-band oscillations in the MOB, which aredriven primarily by respiratory sampling (sniffing) behaviors but alsoby coupling with other brain structures during certain behavioralepochs. Each sampling cycle (“sniff”) consisted of a single sample andsteady-state presentation of sensory input across five gamma cycles ofnetwork activity. The number of gamma cycles per sampling cycle can bearbitrarily determined in order to regulate how much sequential,iterative processing is applied to each sensory sample, but was held atfive for all experiments herein.

It should be noted that these differences between the slower samplingtimescale and the faster processing timescale can be leveraged toimplement “continuous” online sampling, in which each sample can beprocessed using multiple computational iterations prior to digitizingthe next sample. In the present implementation, for example, the Vergaraet al. dataset sampled odorants at 100 Hz—one sample every 10 ms. OnLoihi, operating at 100 kHz, the 200 timesteps (5 gamma cycles) used forthe processing of a single sniff require a total of around 2 ms. As thisis five times faster than the sampling rate of the sensors, there wouldbe no update to sensor state during the time required for five cycles ofprocessing.

Mitral Cells

Each MC was modeled by two compartments—an apical dendrite (AD)compartment that integrated sensor input and generated “spikeinitiation” events when an activation threshold was crossed, and a somacompartment that was excited by spike initiation events in the ADcompartment and synaptically inhibited by spikes evoked in cocolumnarGCs. The soma compartment propagated the AD-initiated spike as an MCaction potential after release from GC inhibition. Accordingly, strongersensory inputs initiated earlier (phase-leading) spikes in MCs, but thepropagation of these spikes could be delayed by inhibition arising frompresynaptic GCs. Distinguishing between these two MC compartmentsfacilitated management of the two input sources and their differentcoding metrics, and reflected the biophysical segregation between themass-action excitation of MC dendritic arbors and the intrinsicregulation of MC spike timing governed by the gamma-band oscillatorydynamics of the MOB EPL.

Sensor activation levels were delivered to the AD compartment of thecorresponding column, which integrated the input during each permissiveepoch of gamma. If and when the integrated excitation exceededthreshold, a spike initiation event was generated and communicated tothe soma compartment. Stronger inputs resulted in more rapid integrationand correspondingly earlier event times. After generating an event, theAD was not permitted to initiate another for the duration of thatpermissive epoch.

A spike initiation event in the AD generated a unit level of excitation(+1) in the soma compartment for the remainder of the permissive epoch.This excitation state caused the MC soma to propagate the spike as soonas it was sufficiently free of lateral inhibition received from itspresynaptic GCs. Accordingly, the main effect of GC synaptic inhibitionwas to modulate MC spike times with respect to the gamma cycle. Theresulting MC spikes were delivered to the classifier as network output,and also were delivered to its postsynaptic GCs.

During the first gamma cycle following odor presentation, when GCinhibition was not yet active, the soma immediately propagated the MCspike initiated in the AD. After propagating a spike, the soma was notpermitted to spike again for the duration of the permissive epoch. Atthe end of the permissive epoch, both the AD and soma compartments werereset to zero for the duration of the inhibitory epoch.

Granule Cells

GCs were modeled as single-compartment neurons,

V=Σ _(k) w _(k) s _(k)  (1)

in which V indicates the excitation level of the GC, w_(k) representsthe excitatory synaptic weight from a presynaptic MC soma k, and k wassummed over all presynaptic MCs. The boolean term s_(k) denotes a spikeat the k-th presynaptic MC soma; s_(k) equals 0 at all times except forthe d-th timestep following a spike in the k-th MC soma, when it was setto 1. Accordingly, d denotes a delay in the receipt of synapticexcitation by a GC following an MC spike. This delay d was randomlydetermined, synapse-specific, and stable (i.e., not plastic); itreflects heterogeneities in spike propagation delays in the biologicalsystem and served to delay GC excitation such that GC spikes were evokedwithin the inhibitory epoch of gamma.

A spike in an MC soma k that was presynaptic to a given GC excited thatGC in proportion to its synaptic weight w_(k). Once GC excitation roseabove a threshold θ_(GC), the GC generated a spike and reset itsexcitation level to zero. Following a spike, the GC was not permitted tospike again for 20 timesteps, ensuring that only one spike could beinitiated in a given GC per gamma cycle. In general, convergentexcitation from multiple MCs was required for GC spike initiation.

Excitatory Synaptic Plasticity

The weights of MC-to-GC synapses were initialized to a value of we.Following an asymmetric, additive spike timing-dependent plasticityrule, these synaptic weights were modified during training following aspike in the postsynaptic GC. Specifically, synapses in which thepresynaptic MC spike preceded the postsynaptic GC spike by 1 timestepwere potentiated by a constant value of δ_(p) whereas all other synapseswere depressed by a constant value of δ_(d). In the present embodiments,we set δ_(p) to 0.05w_(e) and δ_(d) to 0.2w_(e). GC spiking thresholdswere set to Ewe.

The overall effect of this rule was to develop sparse and selectivehigher-order receptive fields for each GC, a process termeddifferentiation. Specifically, repeated coincidences of the same MCspikes resulted in repeated potentiation of the corresponding synapses,whereas synapses of other MCs underwent repeated depression. Individualexcitatory synaptic weights were capped at a value of 1.25w_(e),ensuring that the spiking of differentiated GCs remained sensitive tocoincident activity in a particular ensemble of MCs, the number of whichconstituted the order of the GC receptive field. By this process, odorlearning transformed the relatively broad initial receptive field of aGC into a highly selective one of order M. These higher-order receptivefields reflected correlations between components of individual sensorvectors—i.e., the higher-order signatures of learned odors.Differentiated GCs thereby developed selectivity for particular odorsignatures and became unresponsive to other sensory input combinations.While in principle this GC output can be used directly forclassification purposes, the present algorithm instead deploys it todenoise the spike timing-based MC representation. Because there are manyfewer MCs than GCs, there is a corresponding reduction in bandwidth andenergy consumption by using MCs to communicate the representation forclassification or further processing.

Adult Neurogenesis

The process of GC differentiation permanently depleted the pool ofinterneurons available for recruitment into new odor representations. Toavoid a decline in performance as the numbers of odors learned by thenetwork increased, w_(e) periodically added new, undifferentiated GCinterneurons to the network on a timescale slower than that of thesynaptic plasticity rules—a process directly analogous to adultneurogenesis in the MOB. Specifically, the network was initialized withfive GCs per column, as described above. After the learning of each newodor, an additional set of five undifferentiated GCs was configured inevery column. As with the initial network elements, every MC in thenetwork formed excitatory synapses onto new GCs with a probability of0.2 (20%), and the new GCs all formed inhibitory synapses onto theircocolumnar MCs with initial inhibitory weights of zero.

Inhibitory Synaptic Plasticity

In the neuromorphic model, inhibitory synapses from presynaptic GCs ontotheir cocolumnar MC somata exhibited three functional states. Thedefault state of the synapse was an inactive state I, which exerted noeffect on the MC (i.e., equal to 0). When a spike was evoked in the GC,the synapse transitioned into an inhibitory blocking state B; this statewas maintained for a period of time Δ_(B) that was determined bylearning. While in this state, the synapse maintained a unit level ofinhibition (equal to −1) in the postsynaptic MC soma that inhibitedsomatic spike propagation. The blocking period Δ_(B) therefore governedMC spike latency, and corresponded functionally to the inhibitorysynaptic weight. At the end of the blocking state, the synapsetransitioned to a release state R for 1 timestep, during which itgenerated a unit level of excitation (equal to +1) in the postsynapticMC soma. The synapse then resumed the inactive state. An MC somapropagated a spike when the sum of the excitation and inhibitiongenerated by its apical dendrite and by the synapses of all of itspresynaptic GCs was positive. After spiking once, the MC soma was notpermitted to spike again for the duration of that gamma cycle.

All inhibitory synaptic weights in new GCs were initialized to Δ_(B)=0ts. During training, additionally, the effects of inhibition on MCsomata were suppressed. If an MC AD initiated a spike within thepermissive epoch immediately following a cocolumnar GC spike (in theprevious inhibitory epoch), the blocking period Δ_(B) imposed by that GConto the soma of that MC was modified based on the learning rule

δ_(b)=η(t _(AD) −t _(R))  (2)

where δ_(b) is the change in the blocking period Δ_(B) (inhibitorysynaptic weight), t_(AD) is the time of the MC spike initiation event inthe AD, t_(R) is the time at which the inhibitory synapse switched fromthe blocking state to the release state, and η was the learning rate(set to 1.0 in the one-shot learning studies presented here).Consequently, the synaptic blocking period Δ_(B) was modified duringtraining (rounding up fractions) until the release of inhibition fromthat synapse was aligned with the spike initiation event in the MC AD(FIG. 6B). If the GC spike was not followed by an MC spike initiationevent during the following permissive epoch, the inhibitory weight Δ_(B)of that synapse grew until that MC was inhibited for the entire gammacycle. Inputs from multiple local GCs onto a common MC were applied andmodified independently.

In total, this inhibitory synaptic plasticity rule enabled the EPLnetwork to learn the timing relationships between GC spikes andcocolumnar MC spikes associated with a given odor stimulus, therebytraining the inhibitory weight matrix to construct a fixed-pointattractor around the odor representation being learned. This served tocounteract the consequences of destructive interference in odor stimulipresented during testing. It should be noted that this plasticity ruleeffectively learned the specific ratiometric patterns of activationlevels among MCs that characterized particular odors; consequently, twoodors that activated the same population of MCs, but at differentrelative levels, could be readily distinguished.

Testing Procedures

After training, we tested the network's performance on recognizinglearned odorants in the presence of destructive interference fromunpredictable sources of olfactory occlusion (impulse noise), alone orin combination with variance arising from sampling plume dynamics atdifferent timepoints. All testing was performed with network plasticitydisabled.

The responses of primary olfactory receptors to a given odorant ofinterest can be radically altered by the concomitant presence ofcompeting background odorants that strongly activate or block some ofthe same receptors as the odorant of interest, greatly disrupting theratiometric activation pattern across receptors on which odorrecognition depends. We modeled this occlusion as destructive impulsenoise. Specifically, an occluded test sample was generated by choosing afraction P of the 72 elements of a sensor activity vector and replacingthem each with random values drawn uniformly from the sensors' operatingrange (integer values from 0 to 15). When multiple occluded test sampleswere generated to measure average performance, both the identities ofthe occluded elements and the random values to which they were set wereredrawn from their respective distributions.

Odor plume dynamics comprise a second source of stimulus varianceencountered under natural conditions. To test network performance acrossthis variance, we drew test samples from different timepoints within theodor plumes. Specifically we drew 30 samples per plume at 5 secondintervals between 30 seconds and 180 seconds within the 180 seconddatastreams. After one-shot training with a single sample, we testednetwork performance on the other samples, with and without the additionof impulse noise (FIG. 9).

While certain of the present embodiments focus on one-shot learning, thenetwork can also be configured for few-shot learning, in which itgradually adapts to the underlying statistics of training samples. Inthis configuration, the network learns robust representations even whenthe training samples themselves are corrupted by impulse noise.

Sample Classification

The pattern of MC spikes in each successive gamma cycle was recorded asa set of spikes, with each spike defined by the identity of the activeMC and the spike latency with respect to the onset of that permissiveepoch. Accordingly, five successive sets of spikes were recorded foreach sample “sniff.” When an impulse noise-occluded sample was presentedto the network, the similarities were computed between each of the fiverepresentations evoked by the unknown and each of the network's learnedodor representations In descriptive figures (but not for comparisonswith other methods), the similarity between two representations wasmeasured with the Jaccard index, defined as the number of spikes in theintersection of two representations, divided by the number of spikes intheir union. Specifically, the permissive epoch of a gamma cycleincluded 16 discrete timesteps in which MCs could spike; these 16 binswere used for Jaccard calculations. Test samples were classified as oneof the network's known odorants if the similarity exceeded a thresholdof 0.75 in the fifth (final) gamma cycle. If similarities to multiplelearned odorants crossed the threshold, the odorant exhibiting thegreatest similarity value across the five gamma cycles was picked as theclassification result. If none of the similarity values crossed thethreshold within five gamma cycles, the odorant was classified asunknown. This combination of nearest-neighbor classification andthresholding enabled the network to present “none of the above” as alegitimate outcome. Summary figures each consist of averages across 100independent instantiations of impulse noise, and/or averages across 30different test samples drawn from different timepoints in the datastream(without or with added impulse noise), for each odor in the trainingset.

Benchmarks

We first compared the classification performance of the EPL network tothree conventional signal processing techniques: a median filter (MF), atotal variation filter (TVF), and principal component analysis (PCA;FIG. 10(a)). The MF and TVF are filters commonly used in signalprocessing for reducing impulse noise, while PCA is a standardpreprocessor used in machine olfaction applications. The MF used awindow size of 5, and was implemented with the Python signal processinglibrary scipy.signal. The TVF used a regularization parameter equal to0.5, and was implemented using the Python image processing libraryscikit-image. PCA was implemented using the Python machine learninglibrary scikit-learn; data were projected onto the top five components.

Corrupted input signals also can be denoised by training an autoencoder,a modern rendition of autoassociative networks. We therefore comparedthe performance of the EPL network to a seven-layer deep autoencoderconstructed using the Python deep learning library Keras. The sevenlayers consisted of an input layer of 72 units, followed by five hiddenlayers of 720 units each and an output layer of 72 units. This resultedin a network of 3744 units, identical to the number in the EPL modelwhen trained with ten odors. The network was fully connected betweenlayers, and the activity of each unit in the hidden layers was L1regularized. The network was trained with iterative gradient descentuntil convergence using the Adadelta optimizer with a mean absoluteerror loss function. Its training set consisted of 7000 examples perodorant class. For the same training set, the performance of thisseven-layer autoencoder exceeded that of shallower networks (6-, 5-, 4-,and 3-layer networks were tested).

For direct comparison, the outputs of all of these methods, includingthat of the EPL network, were presented to the same nearest-neighborclassifier for sample classification according to a Manhattan distancemetric. Specifically, for each of the techniques, the output was read asa 72-dimensional vector and normalized such that their elements summedup to a value of unity. (In the case of the EPL network, the spikingoutput in each gamma cycle was read out as a 72-dimensional rank-ordervector and normalized so that the elements summed to unity). Thesimilarity between any two such vectors was measured as (1/(1+d)) whered is the Manhattan distance between the two vectors. Classificationperformance was measured by computing this similarity between the outputof training data samples and those of test data samples. A test datasample was classified according to the identity of the training datasample to which it was most similar, provided that this similarity valueexceeded a threshold of 0.75 (thresholding enabled the inclusion of a“none of the above” outcome).

We trained the DAE in three different ways for fair comparison with EPLnetwork performance. First, the DAE was trained using the same tennon-occluded odor samples that were used to train the EPL model. Theseten samples underwent 1000 training epochs to ensure trainingconvergence. This method assesses DAE performance on “one-sample”learning, for comparison with the one-sample/one-trial learning of theEPL network (FIG. 10(a)). Second, we trained the DAE on multiple impulsenoise-occluded samples, so as to maximize its performance. Specifically,we trained the DAE on 500 to 7000 training samples, where each samplecomprised an independently occluded instance of each of the tenodorants. Each training set was presented for 25 training epochs toensure convergence. The occlusion levels for each training sample weredrawn from the same distribution as the test samples, being randomly anduniformly selected from the range P=[0.2, 0.8]. With this procedure, weshow that the DAE requires 3000 training samples per odorant to achievethe classification performance that the EPL model achieved with 1training sample per odorant (FIG. 10(c)); i.e., the EPL model is 3000times more data efficient than the DAE. Third, we trained the DAE andEPL models first on one odorant (toluene) and then, subsequently, on asecond odorant (acetone) in order to compare the models' sequentialonline learning capabilities. After training on toluene, the DAEclassified test presentations of toluene with high fidelity (FIG. 10(c);left panel). However, over the course of acetone training, thesimilarity between test samples of toluene and the learnedrepresentation of toluene progressively declined (FIG. 10(d)), to thepoint that the DAE network became unable to correctly classify toluene(FIG. 10(c), right panel). In contrast, training the EPL network withacetone exhibited no interference with the preexisting toluenerepresentation (FIG. 10(d), inset). The similarity between test samplesof toluene and the learned representation of toluene was not affected asthe EPL learned all of the ten odorants in sequence (FIG. 10(e)).

Implementation on the Loihi Neuromorphic System

Neuromorphic systems are custom integrated circuits that modelbiological neural computations, typically with orders of magnitudegreater speed and energy efficiency than general-purpose computers.These systems enable the deployment of neural algorithms in edgedevices, such as chemosensory signal analyzers, in which real-timeoperation, low power consumption, environmental robustness, and compactsize are important operational metrics. Loihi, a neuromorphic processordeveloped for research at Intel Labs, advances the state of the art inneuromorphic systems with innovations in architecture and circuitdesign, and a feature set that supports a wide variety of neuralcomputations. Below we provide an overview of the Loihi system and ournetwork implementation thereon.

Loihi is fabricated in Intel's 14-nm FinFET process and realizes a totalof 2.07 billion transistors over a many-core mesh. Each Loihi chipcontains a total of 128 neuromorphic cores, along with three embeddedLakemont x86 processors and external communication interfaces thatenable the neuromorphic mesh to be extended across many interlinkedLoihi chips (FIG. 5B). Each neuromorphic core comprisesleaky-integrate-and-fire compute units that integrate filtered spiketrains from a configurable set of presynaptic units and generate spikeswhen a threshold level of excitation is crossed. Postsynaptic spikesthen are communicated to a configurable set of target units anywherewithin the mesh. A variety of features can be configured in a core,including multicompartment interactions, spike timing-dependent learningrules, axonal conduction delays, and neuromodulatory effects. Allsignals in the system are digital, and networks operate as discrete-timedynamical systems.

We configured each column of our model within one neuromorphic core,thereby using a total of 72 cores on a single chip. Cocolumnar synapticinteractions took place within a core, whereas the global projections ofMC somatic spikes were routed via the intercore routing mesh. Theconfigured network utilized 12.5% of the available neural resources percore and 6% of the available synaptic memory.

Completing one inference cycle (sniff; 5 gamma cycles; 200 timesteps) ofthe 72-core network required 2.75 ms and consumed 0.43 mJ, of which 0.12mJ is dynamic energy. It should be noted that the time required tosolution was not significantly affected by the scale of the problem(FIG. 10(f)), owing to the Loihi architecture's fine-grainedparallelism. This scalability highlights a key advantage of neuromorphichardware for application to computational neuroscience and machineolfaction. Energy consumption also scaled only modestly as network sizeincreased (FIG. 10(g)), owing to the colocalization of memory andcompute and the use of sparse (spiking) communication, which minimizethe movement of data. Using multichip Loihi systems, illustrativeembodiments are readily scalable to hundreds of columns and hundreds ofthousands of interneurons, and can integrate circuit models of theglomerular layer and the piriform cortex with the current EPL network ofthe MOB.

Further illustrative embodiments will now be described with reference toFIG. 11.

These embodiments, like others disclosed herein, provide SNN algorithmsfor signal restoration and identification based on principles extractedfrom the mammalian olfactory system and broadly applicable to input fromarbitrary sensor arrays. For interpretability and development purposes,we here examine the properties of its initial feedforward projection.Like the full algorithm, this feedforward component is fully spiketiming-based, and utilizes online learning based on local synaptic rulessuch as STDP rules. Using an intermediate metric to assess theproperties of this initial projection, the feedforward network exhibitshigh classification performance after few-shot learning withoutcatastrophic forgetting, and includes a “none of the above” outcome toreflect classifier confidence. We demonstrate online learningperformance using a publicly available machine olfaction dataset withchallenges including relatively small training sets, variable stimulusconcentrations, and three years of sensor drift.

The SNN-based online learning algorithms in these embodiments, based onprinciples and motifs derived from the mammalian olfactory system, canaccurately classify noisy high-dimensional signals into categories thathave been dynamically defined by few-shot learning. In order to betterinterpret the basis for the algorithm's capabilities, we focus in thisdescription on the properties of the first feedforward projection,omitting the spike timing-based feedback loop that forms the corenetwork of the full MOB model. Glomerular-layer processing isrepresented here by two preprocessing algorithms, whereas plasticity forrapid learning is embedded in subsequent processing by the EPL network.Information in the EPL network is mediated by patterns of spike timingwith respect to a common clock corresponding to the biological gammarhythm, and learning is based on localized spike timing-based synapticplasticity rules. The algorithm is illustratively implemented in PyTorchfor GPU computation, but is also suitable for implementation onstate-of-the-art neuromorphic computing hardware such as the Intel Loihiplatform. We here demonstrate the interim performance of the feedforwardalgorithm using a well-established machine olfaction dataset withdistinct challenges including multiple odorant classes, variablestimulus concentrations, physically degraded sensors, and substantialsensor drift over time.

The network is based on the architecture of the mammalian MOB. Primaryolfactory sensory neurons (OSNs) express a single odorant receptor typefrom a family of hundreds (depending on animal species). The axons ofOSNs that express the same receptor type converge to a common locationon the surface of the MOB, forming a mass of neuropil called aglomerulus. Each glomerulus thus is associated with exactly one receptortype, and serves as the basis for an MOB column. The profile ofglomerular activation levels across the hundreds of receptor types (˜400in humans, ˜1200 in rats and mice) that are activated by a given odorantconstitutes a high-dimensional vector of sensory input. Within thisfirst (glomerular) layer of the MOB, a number of preprocessingcomputations also are performed, including a high-dimensional form ofcontrast enhancement and an intricate set of computations mediating atype of global feedback normalization that enables concentrationtolerance. The cellular and synaptic properties of this layer also beginthe process of transforming stationary input vectors into spiketiming-based representations discretized by 30-80 Hz gamma oscillations.The EPL, which constitutes the deeper computational layer of the MOB,comprises a matrix of reciprocal interactions between principal neuronsactivated by sensory input (e.g., MCs) and inhibitory interneurons(e.g., GCs). Computations in this layer depend on fine-timescale spiketiming and odor learning, and modify the information exported from theMOB to its follower cortices.

Chemical sensing in machine olfaction is similarly based uponcombinatorial coding; specificity is achieved by combining the responsesof many poorly-selective sensors. In the present algorithm, networkswere defined with a number of columns such that each column receivedinput from one type of sensor in the connected input array. Columns eachcomprised one ET cell and one PG cell to mediate glomerular-layerpreprocessing, and one MC and a variable number of GCs to mediate EPLodorant learning and classification, as illustrated in FIG. 11. Sensoryinput was preprocessed by the ET and PG cells of the glomerular layer(for concentration tolerance), and then delivered as excitation to thearray of MCs, which generated action potentials. Each MC synapticallyexcited a number of randomly determined GCs drawn from across the entirenetwork, whereas activated GCs synaptically inhibited the MC in theirhome column. It should be noted that, in the present embodiments, theseinhibitory feedback weights were illustratively all reduced to zero todisable the feedback loop and EPL attractor dynamics, enablingevaluation of the initial feedforward transformation based on excitatorysynaptic plasticity alone. During learning, the excitatory synapsesfollowed a spike timing-dependent plasticity rule that systematicallyaltered their weights, thereby modifying the complex receptive fields ofrecipient GCs in the service of odor learning. In the presentembodiments, in lieu of the modified spike timing of the MC ensemblethat characterizes the output of the full model, the binary vectordescribing GC ensemble activity in response to odor stimulation (0:non-spiking GC; 1: spiking GC) served as the processed data forclassification. Because we here describe the capacities of the initialfeedforward projection of preprocessed data onto the GC interneuronarray within the EPL—an initial transformation that sets the stage forongoing dynamics not discussed herein—we refer to such an embodiment asthe EPLff network algorithm.

FIG. 11 shows a detailed view of a portion 1100 of the above-describedSNN implementing a neuromorphic algorithm in accordance withillustrative embodiments. The portion 1100 more particularly comprisesEPLff network circuitry. Three columns are depicted in this view, forclarity and simplicity of illustration, but it is to be appreciated thatother columns of the SNN are configured in a similar manner. Scaledsensor output is presented as sensor-scaled input data 1104 in parallelto excitatory ET cells 1105A and inhibitory PG cells 1105B in aglomerular layer of a preprocessor of the SNN. This glomerular-layercircuit performs an unsupervised concentration tolerance preprocessorstep based on the graded inhibition of ET cells 1105A by PG cells 1105B.The concentration-normalized ET cell activity then is presented as inputto their co-columnar MCs 1110. In the EPL, comprising MC interactionswith inhibitory GCs 1112, levels of sensory input are encoded in MCs1110 as a spike time precedence code across the MC population. MCsproject randomly onto GCs 1112 with a connection probability of 0.4.These synaptic connections are plastic, following an STDP rule thatenables GCs 1112 to learn high-order receptive fields. The GC populationconsequently learns to recognize specific odorants by measuring thesimilarity of high dimensional GC activity vectors with the Hammingdistance metric. The SNN in the present embodiments generates aconcentration prediction 1115 for particular input data using a readoutfrom the GCs 1112 as illustrated.

Data preprocessing techniques in these illustrative embodiments will nowbe described in more detail.

Sensor scaling. We defined a set of preprocessing algorithms, any or allof which could be applied to a given data set to prepare it forefficient analysis by the core algorithm. The first of these, sensorscaling, is applied to compensate for heterogeneity in the scales ofdifferent sensors—for example, an array comprising a combination of 1.8Vand 5V sensors. One simple solution is to scale the responses of eachsensor by the maximum response of that sensor. Let x₁, x₂, x₃, . . . ,x_(n) be the responses of n sensors to a given odor and s₁, s₂, s₃, . .. , s_(n) be the maximum response values of those sensors. Then,

$\frac{x_{1}}{s_{1}},\frac{x_{2}}{s_{2}},\frac{x_{3}}{s_{3}},\ldots\mspace{14mu},\frac{x_{n}}{s_{n}}$

represent the sensor-scaled responses. The maximum sensor responsevector S could be predetermined (as in sensor voltages), or estimatedusing a model validation set. Here, we defined S using the modelvalidation set (10% of Batch 1 data) and utilized the same value of Sfor scaling all subsequent learning and inference data. Thispreprocessing algorithm becomes particularly useful when analyzing datafrom arbitrary or uncharacterized sensors, or from arrays of sensorsthat have degraded and drifted nonuniformly over time.

Unsupervised concentration tolerance. Concentration tolerance is animportant feature of mammalian as well as insect olfaction. Changes inodorant concentration evoke nonlinear effects in receptor activationpatterns that are substantial in magnitude and often indistinguishablefrom those based on changes in odor quality. Distinguishingconcentration differences from genuine quality differences appears torely upon multiple coordinated mechanisms within MOB circuitry, but themost important of these is a global inhibitory feedback mechanisminstantiated in the deep glomerular layer. The consequence of thiscircuit is that MC spike rates are not strongly or uniformly affected byconcentration changes, and the overall activation of the MOB networkremains relatively stable. We implemented this concentration tolerancemechanism as the graded inhibition of ET cells by PG cell interneuronsin the MOB glomerular layer, as shown in FIG. 11—a mechanism based uponrecent experimental findings in which ET cells serve as the primarygates of MC activation—and tested its importance empirically on machineolfaction data sets. This concentration tolerance mechanism facilitatesrecognition of odor stimuli even when they are encountered atconcentrations on which the network has not been trained; moreover, oncean odor has been identified, its concentration can be estimated based onthe level of feedback that the network delivers in response to itspresentation. This preprocessing step requires no information aboutinput data labels, and greatly facilitates few-shot learning.

Input from each sensor was delivered directly to ET and PG interneuronsassociated with the column corresponding to that sensor, and theresulting PG cell activity was delivered via graded synaptic inhibitiononto all ET cells within all columns in the network. ET cells in turnthen synaptically excited their corresponding, cocolumnar MCs, asillustrated in FIG. 11. The approximate outcome of this preprocessoralgorithm is as follows: given that x₁ ^(ET), x₂ ^(ET), x₃ ^(ET), . . ., x_(n) ^(ET) denote the responses of ET cells to odor inputs (prior totheir inhibition by PG cells), and x₁ ^(pg), x₂ ^(pg), x₃ ^(pg), . . . ,x_(n) ^(pg) denote the analogous responses of PG interneurons to thesesame inputs, the resulting input to MC somata from ET cells followingtheir PG-mediated lateral inhibition will be

$\begin{matrix}{\frac{x_{1}^{ET}}{\sum x^{pg}},\frac{x_{2}^{ET}}{\sum x^{pg}},\frac{x_{3}^{ET}}{\sum x^{pg}},\ldots\mspace{14mu},\frac{x_{n}^{ET}}{\sum x^{pg}}} & (3)\end{matrix}$

A version of this algorithm has been implemented using spiking networkson IBM TrueNorth neuromorphic hardware.

The core algorithm in these embodiments will now be described in moredetail.

Cellular and synaptic models. We modeled the MCs and GCs as leakyintegrate-and-fire neurons with an update period of 0.01 ms. Theevolution of the membrane potential v of MCs and GCs over time wasdescribed as

$\begin{matrix}{{\tau\frac{dv}{dt}} = {{- v} + {IR}}} & (4)\end{matrix}$

where τ=r_(m)c_(m) was the membrane time constant and r_(m) and c_(m)denote the membrane resistance and capacitance respectively. For MCs,the input current I corresponded to sensory input received from ET cells(after preprocessing by the ET and PG neurons of the glomerular layer asillustrated in FIG. 11), whereas for GCs, 1 constituted the totalsynaptic input from convergent presynaptic MCs. In GCs, the parameter Rwas set to equal r_(m), whereas in MCs it was set to r_(m)/r_(shunt)where r_(shunt) was the oscillatory shunting inhibition of the gammaclock (described below). When v≥v_(th), where v_(th) denotes the spikethreshold, a spike event was generated and v was reset to 0. The totalexcitatory current to GCs was modeled as

I=g _(w)(E _(n) −v)  (5)

where E_(n) was the Nernst potential of the excitatory current (+70 mv),v was the GC membrane potential, and

$g_{w} = {\sum\limits_{1 - 1}^{n}{w_{i}g_{\max}\frac{\tau_{1}\tau_{2}}{\tau_{1} - \tau_{2}}\left( {e^{\frac{- {({t - t_{i}})}}{\tau_{1}}} - e^{\frac{- {({t - t_{i}})}}{\tau_{2}}}} \right)}}$

describes the open probability of the AMPA-like synaptic conductances.Here, denotes presynaptic spike timing, w_(i) denotes the synapticweight, and g_(max) is a scaling factor.

The parameters c_(m), r_(m), r_(shunt), E_(n), g_(max), τ₁, and τ₂ weredetermined only once each for MCs and GCs using a synthetic data set andremained unchanged during the application of the algorithm to realdatasets. The value of w_(i) at each synapse also was set to a fixedstarting value based on synthetic data, but was dynamically updatedaccording to the STDP learning rule. The spiking thresholds v_(th) ofMCs and GCs were determined by assessing algorithm performance on thetraining and validation sets. Because we observed that usingheterogeneous values of v_(th) across GCs improved performance, thevalues of v_(th) were randomly assigned across GCs from a uniformdistribution.

Gamma clock and spike precedence code. Oscillations in the local fieldpotential are observed throughout the brain, arising from thesynchronization of activity in neuronal ensembles. In the MOB,gamma-band (30-80 Hz) oscillations are associated with the coordinatedperiodic inhibition of MCs by GCs that constrains MC spike timing,thereby serving as a common clock. For this work, we modeled a singlecycle gamma oscillation as a sinusoidal shunting inhibition r_(shunt)delivered onto all MCs,

$\begin{matrix}{r_{shunt} = {{{- 3.8}*{\cos\left( \frac{2\pi*f*t}{1000} \right)}} + 5}} & (6)\end{matrix}$

where f is the oscillation frequency (40 Hz) and t is the simulationtime. We used a spike precedence coding scheme for MCs where earlier MCspike phases correspond to stronger sensor input and are correspondinglymore effective at growing and maintaining spike timing-dependent plasticsynapses. In the full model, the gamma clock serves as the iterativebasis for the attractor; for present purposes in the EPLff context itserved only to structure the spike times of active MCs converging ontoparticular GCs (precedence coding), and thereby to govern the changes inexcitatory synaptic weights according to the STDP rule.

Connection topology. MC lateral dendrites support action potentialpropagation to GCs across the entire extent of the MOB, whereasinhibition of MCs by GCs is more localized. Excitatory MC-GC synapseswere initialized with a uniformly distributed random probability cp ofconnection and a uniform weight w₀; synaptic weights were modifiedthereafter by learning. The initial connection probability cp wasdetermined using a synthetic data set, and was set to cp=0.4 in thepresent simulations. For present purposes, as noted above, GC-MCinhibitory weights were set to zero to disable attractor dynamics.

STDP rule. We used a modified STDP to regulate MC-GC excitatory synapticweight modification. Briefly, synaptic weight changes were initiated byGC spikes and depended exponentially upon the spike timing differencebetween the postsynaptic GC spike and the presynaptic MC spike. When apresynaptic MC spike preceded its postsynaptic GC spike within the samegamma cycle, w for that synapse was increased; in contrast, when MCspikes followed GC spikes, or when a GC spike occurred without apresynaptic MC spike, w was decremented. Synaptic weights were limitedby a maximum weight w_(max). The pairing of STDP with MC spikeprecedence coding discretized by the gamma clock generated a “k winnerstake all” learning rule, in which the value of k depended substantiallyon the GC spike threshold v_(th) and the maximum excitatory synapticweight w_(max). Under this rule, activated GCs were transformed fromnonspecialized cells receiving weak inputs from a broad and randomdistribution of MCs into specialized, fully differentiated neurons thatresponded only to coordinated activation across a specific ensemble of kMCs. Under all training conditions, for present purposes, we set a highlearning rate such that, after one cycle of learning, each of thesynapses could have one of only three values: w₀, w_(max), or 0.

The STDP parameters were similar to those described for a synthetic dataset in Ayon Borthakur and Thomas A. Cleland, “A neuromorphic transferlearning algorithm for orthogonalizing highly overlapping sensor arrayresponses,” in 2017 ISOCS/IEEE International Symposium on Olfaction andElectronic Nose (ISOEN), pp. 1-3, 2017. Among these, only the maximumsynaptic weight w_(max) was tuned based on validation set performance.For this feedforward implementation, online learning without therequirement of storing training data yielded its best validation setperformance when w_(max)=w₀, such that learning was limited to long-termsynaptic depression.

Classification. For the classification of test odorants in this reducedfeedforward EPLff implementation, we calculated the Hamming distancebetween the binary vectors of GC odorant representations. Specifically,for every input, GCs generated a binary vector based upon whether the GCspiked (1) or did not spike (0). We matched the similarity of test setbinary vectors with the training set vector(s) using the Hammingdistance and classified the test sample based upon the label of theclosest training sample. Alternatively, an overlap metric between GCactivation patterns also was calculated; results based on this methodwere reliably identical to those of the Hamming distance. Classificationwas set to “none of the above” if the Hamming distance of the GC binaryvectors was greater than 0.5, or if the overlap metric was less than0.5.

We tested our algorithm on the publicly available UCSD gas sensor driftdataset, slightly reorganized to better demonstrate online learning. Theoriginal dataset contains 13910 measurements from an array of 16 polymerchemosensors exposed to 6 gas-phase odorants spanning a wide range ofconcentrations (10-1000 ppmv) and distributed across ten batches thatwere sampled over a period of three years to emphasize the challenge ofsensor drift over time. Owing to drift, the sensors' output statisticschange drastically over the course of the ten batches; between thisproperty, the six different gas types, and the wide range ofconcentrations delivered, this dataset is well suited to test thecapabilities of the present algorithm without exceeding the learningcapacity of its feedforward architecture as illustrated in FIG. 11. Forthe online learning scenario, we sorted each batch of data according tothe odorant trained, but did not organize the data according toconcentration. Hence, each training set comprised 1 to 10 odorantstimuli of the same type but at randomly selected concentrations. Testsets always included all six different odorants, again at randomlyselected concentrations. For sensor scaling and the fine-tuning of thealgorithm, we used 10% of the Batch 1 data as a validation set. The sixodorants in the dataset are, in the order of training used herein:ammonia, acetaldehyde, acetone, ethylene, ethanol, and toluene. Batches3-5 included only 5 different odorant stimuli, omitting toluene.

Eight features per chemosensor were recorded in the UCSD dataset,yielding a 128-dimensional feature vector. However, we chose to use onlyone feature per sensor in our analysis (the steady state responselevel), for a total of 16 features. We imposed this restriction tochallenge our algorithm, and because generating features from raw datarequires additional processing, energy and time, all of which can impairthe effectiveness of field-deployable hardware. It should be noted,however, the sensor scaling and concentration tolerance preprocessorsdescribed above would enable the EPLff network to utilize the full128-dimensional dataset without specific adaptations other thanexpanding the number of columns accordingly.

Results of the above-noted testing of the present embodiments will nowbe described.

Data preprocessing. All sensory input data were preprocessed beforebeing presented to the network. First, sensor scaling was applied toweight the sixteen sensors equally in subsequent computations. The meanraw responses of the sixteen sensors differed widely, with some sensorsexhibiting an order of magnitude greater variance than others across theten odorants tested. Sensor scaling mitigated this effect by scalingeach sensor's gain such that the dynamic ranges of all sensors acrossthe test battery were effectively equal. This process enabled eachsensor to contribute a comparable amount of information to subsequentcomputations (up to a limit imposed by each sensor's signal to noiseratio), and improved network performance by maintaining consistent meanactivity levels across test odorants.

Since each odorant was presented at a wide range of randomly selectedconcentrations, the response of the sensor array to a given odorantvaried widely across presentations. Application of the unsupervisedconcentration tolerance preprocessor sharply and selectively reduced theconcentration-specific variance among responses to presented odorants.These preprocessed odorant signatures then were presented to the plasticEPLff network for training or classification. Notably, this preprocessorstep greatly facilitated cross-concentration odorant recognition, evenenabling the accurate classification of samples presented atconcentrations that were not included in the training set. This wasparticularly important for one- and few-shot learning, in which thenetwork was trained on just one or a few exemplars (respectively), atunknown concentration(s), such that most of the odorants in the test setwere presented at concentrations on which the network had never beentrained.

The sensor scaling preprocessor (retaining the scaling factorsdetermined from the 10% validation set of Batch 1), combined with thenormalization effects of the subsequent concentration tolerancepreprocessor, had the additional benefit of restoring the dynamic rangeof degraded sensors in order to better match classifier networkparameters. Because of this, the network did not need to bereparameterized to effectively analyze the responses of the degradedsensors in the later batches of this dataset. Compared to the raw sensoroutput of Batch 1 (collected from new sensors), the raw sensor output ofBatch 7 (collected after 21 months of sensor deterioration) was reducedto roughly a third of its original range. Sensor scaling mitigated thiseffect by magnifying sensor responses into the dynamic range expected bythe network. Subsequent preprocessing for concentration toleranceeffectively reduced concentration-specific variance, revealing a set ofodorant profiles that, while qualitatively dissimilar to their profilesbased on the same sensors 21 months prior, appear only modestly degradedin terms of their distinctiveness from one another.

For many machine olfaction applications, it is useful to estimate theconcentrations of gases in the vicinity of the sensors. We sought to usethe information extracted from the concentration tolerance preprocessorto estimate the concentrations of test samples after classification. Theconcentration estimation curve was a function of both odorant identityand the total sensor response profile. Using the sum of the 16 sensorresponses (S), we fitted an odorant-specific quadratic curve for animplicit model of response profiles across concentrations C: C=ax²+b,where the parameters a and b were determined from the training set. Themean absolute error (MAE) of the prediction (in ppmv) was estimated as

$\begin{matrix}\frac{\sum\limits_{n}{{C_{pred} - C_{actual}}}}{n} & (7)\end{matrix}$

where n denotes the total number of samples. For the five-shot trainingof Batch 1 (i.e., five random samples drawn from Batch 1 for eachodorant), the MAE was 35.14 units. This error was reduced to 23.35 forten-shot learning. Similarly, the MAE for Batch 7 decreased from 76.60(five-shot) to 58.18 (ten-shot). The parallel network architecture inthis embodiment advantageously provides an estimate of concentrationalong with concentration tolerance.

Online learning. Unlike biological odor learning, artificial neuralnetworks optimized for a certain task tend to suffer from catastrophicforgetting, and the pursuit of online learning capabilities in deepnetworks is a subject of active study. In contrast, the EPLff learningnetwork described herein naturally resists catastrophic forgetting,exhibiting powerful online learning using a fast spike timing-basedcoding metric. Moreover, we include a “none of the above” outcome whichpermits classification only above a threshold level of confidence.Hence, after being trained on one odorant, the network could identify atest sample as either that odorant or “none of the above.” Aftersubsequently training the network on a second odorant, it could classifya test sample as either the first trained odorant, the second trainedodorant, or “none of the above.” This online learning capacity enablesad hoc training of the network, with intermittent testing if desired,with no need to train on or even establish the full list of classifiableodorants in advance. It also facilitates training under missing dataconditions (e.g., batches 3-5 contain samples from only five odorants,unlike the other batches which include six odorants), and could beutilized to trigger new learning in an unsupervised exploration context.Finally, once learned, the training set data need not be stored.

To analyze the 16-sensor UCSD dataset, we constructed a 16-columnspiking network with 4800 GC interneurons and a uniformly random MC-GCconnection probability cp=0.4. This number of GCs was selected becauseit was the smallest network that achieved asymptotic performance on thevalidation dataset (Batch 1, one-shot learning). We then trained thisnetwork on ammonia using ten different few-shot training schemes:one-shot, two-shot, three-shot, up through ten-shot in order to measurethe utility of additional training. Test data (across all trainedodorants and all concentrations in the dataset) were classified with100.0% accuracy in all cases. We subsequently trained each of thesetrained networks on acetaldehyde, using the same number of trainingtrials in each case. After one-shot learning of acetaldehyde, thenetwork classified all trained odorants with 99.61±0.28% accuracy(average of three runs). After subsequent one-shot learning of acetone,classification performance was 95.65±0.19%; after ethylene, 96.06±0.17%;after ethanol, 90.94±0.0%, and finally, after one-shot training on thesixth and final odorant, toluene, test set classification performanceacross all odorants was 90.27±0.12%. Multiple-shot learning generallyproduced correspondingly higher classification performance as thetraining regimen expanded. Classification using an overlap metric ratherthan the Hamming distance yielded almost identical results. It should benoted that classification performance did not catastrophically declineas additional odorants were learned in series, particularly whenhigher-quality sensors were used or when larger multiple-shot trainingsets were employed. These results illustrate that the EPLff network,even in the absence of the full model's recurrent component, exhibitstrue online learning.

The availability of data in the UCSD dataset from over three years ofsensor deterioration enabled the testing of this online learningalgorithm with both fresh and degraded sensor arrays. Classificationresults from the same procedures described above but using progressivelyolder and more degraded sensors indicated that classificationperformance declined overall as the sensors deteriorated in laterbatches, but could be substantially rescued by expanding the trainingregimen from one-shot to few-shot learning. Overall, multiple-shottraining reliably improved classification performance, though theresidual variance across different training regimes suggests that therandom selection of better or poorer class exemplars for training(particularly noting the uncontrolled variable of concentration) exerteda measurable effect on performance.

Batch 10 of the UCSD dataset poses a relatively challengingclassification problem. To produce it, the sensors were intentionallydegraded and contaminated by turning off sensor heating for five monthsfollowing the production of Batch 9 data. Prior work with this datasethas achieved up to 73.28% classification performance on Batch 10,without online learning and using a highly introspective approachtailored for this specific dataset. In contrast, ten-shot learning onBatch 10 using the present EPLff algorithm achieved 85.43%classification accuracy.

To compare the EPLff network's resistance to catastrophic forgettingagainst an existing standard method, we built a 16-input multi-layerperceptron (MLP) comprising 16 input units for raw sensor input (ReLuactivation), 4800 hidden units (ReLu activation), and 6 output units forodorant classification. The MLP was trained using the Adam optimizerwith a constant learning rate of 0.001. Since there was nostraightforward way of implementing “none of the above” in an MLP, theMLP was only trained using two or more odorants. After initial,interspersed training on two odorants from Batch 1, the MLP classifiedtest odorants at high accuracy (99.41±0.0%; average of three runs).However, its classification accuracy dropped sharply after thesubsequent, sequential learning of odorant 3 (30.61±0.0% accuracy),odorant 4 (16.24±9.29%), odorant 5 (18.13±0.0%), and odorant 6(15.99±0.0%). Catastrophic forgetting is a well-known limitation ofMLPs, and is presented here simply to quantify the contrast in onlinelearning performance between the EPLff implementation and a standardnetwork of similar scale.

Online reset learning for mitigating sensor drift. One of the mostchallenging problems of machine olfaction is sensor drift, in which thesensitivity and selectivity profiles of chemosensors gradually changeover weeks to months of use or disuse. Efforts to compensate for thisdrift have taken many forms, from simply replacing sensors to designinghighly introspective or specific corrective algorithms. For example, oneapproach requires the nonrandom, algorithmically guided selection ofrelevant samples across batches and/or the utilization of test data asunlabeled data for additional training. Despite some partial successesin these approaches, the real-world challenge of sensor drift is afundamentally ill-posed problem, in which the rapidity and nature offunctional drift is highly dependent on the idiosyncratic chemistry ofindividual sensors and specific sensor-analyte pairs.

A practical solution to this challenge is to retrain the network asneeded to maintain performance, leveraging its rapid, online learningcapacity. Specifically, MC-GC synaptic weights are simply reset to theiruntrained values and the network then is rapidly retrained using the new(degraded) sensor response profiles (reset learning). Retraining is nota new approach, of course, but overtly choosing a commitment toheuristic retraining as the primary method for countering sensor driftis important, as it determines additional criteria for real-world devicefunctionality that candidate solutions should address, such as the needfor rapid, ideally online retraining in the field and potentially atolerance for lower-fidelity training sets. Specifically, retraining atraditional classification network may require:

1. Prior knowledge of the number of possible odor classes to beidentified,

2. A sufficiently large and representative training set incorporatingeach of these classes,

3. The retuning of network hyperparameters to match the alteredcharacteristics of the degraded sensors, requiring an indeterminatenumber of training iterations.

The EPL network is not constrained by the above requirements. Asdemonstrated above, it can be rapidly retrained using small samples ofwhatever training sets are available and then be updatedthereafter—including the subsequent introduction of new classes. Thestorage of training data for retraining purposes is unnecessary as thenetwork does not suffer from catastrophic forgetting. Finally, thepresent network does not require hyperparameter retuning. Here, only theMC-GC weights were updated during retraining (using the same STDP rule);sensor scaling factors and all other parameters were ascertained once,using the 10% validation set of Batch 1, and held constant thereafter.Moreover, the “none of the above” classifier confidence featurefacilitates awareness of when the network may require retraining; anincrease in “none of the above” classifications provides an initial cuethat then can be evaluated using known samples.

To assess the efficacy of this approach, we tested the EPLff algorithmon the UCSD dataset framed as a sensor drift problem. The procedure forthis approach, and consequently the results, are similar to thosedescribed above. It should be noted that the sensor scaling factors andnetwork parameters were tuned only once, using the validation set fromBatch 1, on the theory that the concept of rapid reset was incompatiblewith a strategy of re-optimizing multiple network hyperparameters.Hence, no parameter changes were permitted, other than the MC-GCexcitatory synaptic weights that were updated normally during trainingaccording to the STDP rule. As described above, Batch 1 training samplesfrom all six odorants again were presented to the network in an onlinelearning configuration, and classification performance then was assessedby Batch 1 test data. MC-GC synaptic weights then were reset to thedefault values (the reset), after which Batch 2 training samples werepresented to the network in the same manner, followed by testing withBatch 2 test data including all odorants and concentrations. We repeatedthis process for batches 3-10. We also assessed post-resetclassification performance across all batches based on a maximally rapidreset (i.e., one-shot learning) and compared this to performance afterexpanded training protocols up through ten-shot learning. In general,while modest increases in classification accuracy were observed when thetraining set size was larger, these results demonstrate scalability,showing that the EPLff algorithm classifies large sets of test data withreasonable accuracy even based on small training sets and lackingcontrol over the concentrations of presented odorants.

These illustrative embodiments provide neural network algorithms thatachieve superior classification performance in an online learningsetting while not being specifically tuned to the statistics of anyparticular dataset. This property, coupled with its few-shot learningcapacity and SNN architecture, renders it particularly appropriate forfield-deployable devices based on learning-capable SNN hardware,recognizing that the interim use of the Hamming distance fornearest-neighbor classification in the present EPLff framework can bereplaced with other metrics. This algorithm is inspired by thearchitecture of the mammalian MOB, but is comparably applicable to anyhigh-dimensional dataset that lacks internal low-dimensional structure.

The present EPLff incarnation of the network utilizes one or morepreprocessor algorithms to prepare data for effective learning andclassification by the core network. Among these is an unsupervisedconcentration tolerance algorithm derived from feedback normalizationmodels of the biological system, a version of which has been previouslyinstantiated in SNN hardware. Inclusion of this preprocessor enables thealgorithm in illustrative embodiments to quickly learn reliablerepresentations based on few-shot learning from odorant samplespresented at different and unknown concentrations. Moreover, the networkthen can generalize across concentrations, correctly classifying unknowntest odorants presented at concentrations on which the network was nevertrained, and even estimating the concentrations of these unknowns.

The subsequent, plastic EPL layer of the network is based on ahigh-dimensional projection of sensory input data onto a network ofinterneurons known as GCs. In the present feed-forward implementation,our emphasis is on the roles and capacities of two sequentialpreprocessor steps followed by the STDP-driven plasticity of theexcitatory MC-GC synapses. Other embodiments can include the feedbackarchitecture of the original model while enabling a more sophisticateddevelopment of learned classes within the high-dimensional projectionfield. Even in its present feedforward form, however, the EPLffalgorithm exhibits (1) rapid, online learning of arbitrary sensoryrepresentations presented in arbitrary sequences, (2) generalizationacross concentrations, (3) robustness to substantial changes in thediversity and responsivity of sensor array input without requiringnetwork reparameterization, and, by virtue of these properties, iscapable of (4) effective adaptation to ongoing sensor drift via a rapidreset-and-retraining process termed reset learning. This capacity forfast reset learning represents a practical strategy for field-deployabledevices, in which a training sample kit could be quickly employed in thefield to retune and restore functionality to a device in which thesensors may have degraded. It should be noted that, for such purposes,the EPLff algorithm was not, and need not be, crafted to the statisticsof any particular data set, nor was the network pre-exposed to testingset data.

Because field-deployable devices require a level of generic readinessfor undetermined or underdetermined problems, and these EPLff propertiesfavor such readiness, we have emphasized the portability of thesealgorithms to neuromorphic hardware platforms that may come to drivesuch devices. Interestingly, many of the features of the biologicalolfactory system that have inspired this design are appropriate for suchdevices. Spike timing and event-based algorithms are attractivecandidates for compact, energy-efficient hardware implementation. Spiketiming metrics can compute similar transformations as analogue andrate-based representations; indeed, it has been proposed that spikebased computations could in principle exhibit all of the computationalpower of a universal Turing machine. Spike timing-dependent plasticityis a localized learning algorithm that is highly compatible with thecolocalization of memory and compute principle of neuromorphic design,and its theoretical capacities have been thoroughly explored in diverserelevant contexts. Our biologically constrained approach to algorithmdesign also provides a unified and empirically verified framework toinvestigate the interactions of these various algorithms and informationmetrics, to better interpret and apply them to artificial networkdesign.

In illustrative embodiments, we provide artificial learning networks toreplicate some of the most powerful capabilities of the biologicalolfactory system, in particular its capacity for rapid online learningand the fast and effective classification of learned odorants despiteongoing changes in sensor properties and the unpredictability of odorconcentrations. Other embodiments can extend this framework toincorporate the feedback dynamics of the biological system, increase thedimensionality of sensor arrays, and provide more sophisticatedbiomimetic classifiers.

Additional aspects of illustrative embodiments will now be describedwith reference to FIG. 12.

The mammalian olfactory system learns rapidly from very few examples,presented in unpredictable online sequences, and then recognizes theselearned odors under conditions of substantial interference withoutexhibiting catastrophic forgetting. We have developed, in theillustrative embodiments to be described below, a brain-mimeticalgorithm that replicates these properties, provided that sensory inputsadhere to a common statistical structure. However, in natural,unregulated environments, this constraint cannot be assured. We herepresent a series of signal conditioning steps, inspired by the mammalianolfactory system, that transform diverse sensory inputs into aregularized statistical structure to which the learning network can betuned. This preprocessing enables a single instantiated network to beapplied to widely diverse classification tasks and datasets—hereincluding gas sensor data, remote sensing from spectral characteristics,and multi-label hierarchical identification of wild species—withoutadjusting network hyperparameters.

The mammalian olfactory system learns and recognizes odors of interestunder suboptimal circumstances and in unpredictable environments.Real-world odor stimuli vary in their concentrations and qualities, andare typically encountered in the presence of unpredictableconfigurations of competing background odors that can substantiallyocclude the profile of sensory receptor activation on which odor qualityrecognition nominally depends. Moreover, odor learning is rapid, andmultiple odors can be learned in arbitrary sequences (online learning)without their learned representations interfering with one another(causing catastrophic forgetting) and without training data beingsomehow stored to maintain or restore learning performance. Altogether,this suite of sensory sampling challenges constitutes the problem thatwe refer to herein as “learning in the wild.”

The present embodiments provide example SNN algorithms for learning andidentifying chemosensor array responses and other intrinsicallyhigher-dimensional signals, based on the architecture of the mammalianMOB. Briefly, primary chemosensory neurons expressing a single type ofreceptor converge to common locations on the MOB surface, there formingclusters of neuropil called glomeruli. Activity in these glomerularnetworks then is sampled and processed by second-order principal neuronsand multiple classes of interneurons. Glomerular activation profilesacross hundreds of receptor types (˜1200 in rodents) constitute highdimensional vectors describing odor qualities embedded in multiplesources of noise.

It should be noted that glomerular-layer network interactions performmultiple signal conditioning tasks on raw chemosensory inputs.Recognizing odor stimuli across wide concentration ranges, for example,depends on the coordination of multiple computational elements,including a global inhibitory feedback loop within the MOB glomerularlayer that limits concentration-dependent heterogeneity in the activityof MOB principal neurons. A version of this input normalizationalgorithm has been implemented on the IBM TrueNorth neuromorphichardware platform.

Other embodiments of example SNN algorithms for machine olfactiondisclosed herein, illustratively implemented on Intel Loihi, learnrapidly from one or few shots, resist catastrophic forgetting, andclassify learned odors under high levels of impulse noise. Moreover, theinterpretability of these algorithms enables the causes of theclassification to be ascertained post hoc, in principle enabling theidentification of the specific combinations of input features thatdetermine a sample's classification. More generalized versions of thismodel relax control over key parameters in order to develop anexperience-dependent metric of similarity for purposes of hierarchicalclassification. However, the plastic network at the core of thisgeneralized algorithm is sensitive to the statistical parameters ofsensory input, potentially requiring parameter retuning in order tomaintain effective classification performance when the input statisticschange. We instead implement a consistent set of adaptive signalconditioning mechanisms that illustratively enable any sensor arrayinput profile to be accepted by a given instantiated network forlearning and high-fidelity classification under noise without requiringparameter retuning. This strategy enables multiple, statisticallydiverse input signals to each be encountered, learned, and classified bythe same network—an important capacity for an artificial sensory systemdeployed into an unknown “wild” environment.

An example algorithm adaptation for “learning in the wild” will now bedescribed in more detail with reference to FIG. 12.

FIG. 12 shows a schematic overview of brain-mimetic model. Animplementation 1200 of a neuromorphic algorithm using an SNN in thisembodiment comprises a core learning network 1201 driven by inputreceived by a data sampling stage 1204 and preprocessed by a pluralityof preprocessors 1205. The preprocessors 1205 include multiple signalconditioning functions attributed to glomerular layer circuitry in thebiological system, including normalization, contrast enhancement, andstatistical regularization. The core learning network 1201 comprises aninhibitory feedback loop between principal neurons 1210 and interneurons1212 in which sensory information is conveyed by the phases of principalneuron spike times with respect to the underlying gamma cycle; learnedpatterns form attractors that classify test samples, as describedelsewhere herein. For purposes of the present embodiments, thisinhibitory feedback was disabled and the patterns of interneuronactivation were read out directly. Classification was estimated based onthe minimum Hamming distance between test sample and learned ensemblesin the interneuron representation.

The feedback loop comprising the core learning network 1201 recruitspopulations of interneurons during learning to represent higher-orderstimulus features, as described previously herein. To explicitlyrepresent stimulus similarity (a prerequisite for constructinghierarchical representations on this metric), these recruitedpopulations are permitted to overlap in their representation of similarinput stimuli—a goal that requires relaxing control over interneuronrecruitment. However, this poses a challenge, in that differentlystructured sensory inputs can be poorly suited for the parameterizednetwork. Sensors in the array that are mismatched to the environment orto one another, sensory input profiles that differ substantially in meanamplitudes (e.g., higher or lower analyte concentrations), or even inputprofiles that are broader and flatter or steeper and narrower thanexpected all have the potential to disrupt learning and classificationperformance. In lieu of retuning network hyperparameters, we sought toconstruct a network architecture that could learn and classify inputpatterns irrespective of their statistical properties. That is,“learning in the wild” in some embodiments configures a singleparameterized network to be able to learn and classify any set ofrelevant signal patterns that it may encounter.

We here present two elements of network architecture, inspired by thebiological olfactory system, that enable “learning in the wild.” First,we present a series of signal conditioning preprocessors, based onelements of MOB glomerular-layer circuitry, that effectively normalizeand regularize sensory input patterns. Second, we show that theimplementation of heterogeneity in key network parameters furtherbroadens network tolerance and improves classification performance. Toillustrate these effects more clearly, in describing the presentembodiments we omit the inhibitory feedback loop that governs theattractor dynamics of the core learning network, and instead focus on anintermediate estimate of classification accuracy derived from the firstprojection of the preprocessed input stream onto the interneurons of thecore network (i.e., the EPLff component described above and illustratedin FIG. 12). We also describe the profiles of interneuron recruitment asan indicator of the statistical similarities among input signals afterpreprocessing, and by extension the adaptiveness of theserepresentations for the fixed hyperparameters of the core learningnetwork.

Various features of preprocessors utilized in the present embodimentswill now be described in more detail.

We implemented three preprocessors that were applied in sequence tosampled input vectors. Among these, the second (intensity normalization)is directly inspired by glomerular-layer operations in the MOB, and thethird (heterogeneous duplication) makes use of known circuit motifs inthe MOB to which no clear function has previously been attributed.

Sensor scaling. Sensor scaling enables the inclusion of heterogeneoussets of sensors or feature values that may be drawn from differentscales of measurement. Based on a small sample of inputs (validationset), this preprocessor estimates the range of values received from eachsensor and scales each sensor value accordingly. Because samples cannotbe guaranteed to include the full range of values that a sensor maydeliver, this step does not comprise idealized scaling, butorder-of-magnitude approximate scaling that prevents a subset of inputsfrom inappropriately dominating network plasticity. To enhance featurevalue differences, the scaled parameters then are multiplied by anequidimensional vector with values drawn from a uniform distributionbetween 0.5 and 1.0; once defined, these vector values are a constantattribute of an instantiated network.

Unsupervised intensity normalization. For some input streams, stimulusintensity can interfere with identity. For example, increasedconcentrations of chemical analytes will nonuniformly increase theresponses of array chemosensors, which impairs analyte recognitionacross concentrations. In the biological system, it has been proposedthat multiple coordinated mechanisms serve to reduce the impact ofintensity differences (i.e., yielding concentration tolerance, orconcentration invariance), with the remaining uncompensated intensityeffects being learned as part of the characteristic variance of thatstimulus. We adopted this principle, implementing a nonspecificinhibitory feedback mechanism inspired by the deep glomerular layer ofthe olfactory system and comparable to one previously implemented inneuromorphic hardware. This preprocessor enables the recognition ofodorant signatures presented at a range of untrained concentrations,even under few-shot learning conditions. Intensity normalization in thebiological system also is required for regulated high-dimensionalcontrast enhancement, although the latter algorithm was not incorporatedinto the present simulations.

Heterogeneous duplication. Despite sensor scaling and intensitynormalization, the different distributions of activity levels across thearray of inputs still could disrupt the performance of the coreattractor in the generalized network model, most prominently byrecruiting widely divergent numbers of interneurons during learning. Toaddress this problem without resorting to retraining networkhyperparameters, we duplicated each input across a number of excitatoryfeedforward interneurons (e.g., five) and then randomly projected theactivity of these interneurons onto a similar number of principalneurons, as previously described herein in conjunction with FIG. 4.Because the number of processing columns of the core learning network isdetermined by the number of principal neurons, this also expanded thedimensionality of the network. The integration and synaptic propertiesof both cell types were heterogeneous across the duplicates, drawnrandomly from a defined range during network instantiation. Thisfeedforward heterogeneous duplication with random projectionsregularized the statistical distribution of input levels into aconsistent range, enabling a single parameterization of the core networkto be effective across a wide range of poorly-behaved inputs.

Interestingly, the need for statistical regularization of afferent inputactivity has not yet been recognized as a problem in the biologicalolfactory system. It may be that the biological system is tolerant ofstatistically diverse inputs via other mechanisms that have yet to beelucidated, but it is nevertheless intriguing that this feedforwardprojection motif is the dominant mechanism of sensory sampling in thebiological MOB. Specifically, convergent primary sensory neuronsprimarily excite ET cells within a glomerulus (along with inhibitory PGcells), and these ET cells then in turn excite the principal neurons ofthat glomerulus. This indirect pathway has been shown to be the dominantpath of afferent excitation, with direct OSN-to-principal neuronexcitation being relegated to a considerably smaller role.

Goodness of preprocessing metric, g_(p). The preprocessor sequencedescribed above regularized widely diverse input signals into a commonstatistical distribution to which the core network was optimized.Well-regularized sensory inputs recruit consistent numbers ofinterneurons into the representation during learning, and activateappropriate interneuron ensembles during testing. To assess thefunctional adequacy of preprocessing, we developed a goodness ofpreprocessing metric, g_(p), as a measure of the consistency ofinterneuron recruitment efficacy across a heterogeneous range ofsamples:

$\begin{matrix}{g_{p} = {{\min\left( {{\min(v)},1} \right)}^{*}\frac{\sum\frac{v_{i}}{\max(v)}}{\dim\mspace{11mu} v}}} & (8)\end{matrix}$

where v is an integer vector of interneuron spike counts and dim vdenotes the number of samples under consideration. This equation has twofactors. First, the no-spike penalty

min(min(v),1)  (9)

is zero if any of the stimuli presented fail to activate anyinterneurons at all; otherwise its value is unity. Second, theinterneuron activation similarity index

$\begin{matrix}\frac{\sum\frac{v_{i}}{\max(v)}}{\dim\mspace{11mu} v} & (10)\end{matrix}$

reflects the similarity of interneuron recruitment levels across allstimulus presentations (i.e., across multiple different stimuli,potentially also including a range of stimulus intensities orconcentrations). These two factors together generate a value of g_(p)between 0 and 1. A g_(p) value approaching unity indicates that all teststimuli activate approximately the same nonzero number of interneurons;lower values indicate that different stimuli recruit substantiallydifferent numbers of interneurons, or none at all, which may impair theperformance of a given core network for some of these stimuli.

The core learning network in these embodiments will now be furtherdescribed.

The core learning network comprises a recurrent excitatory-inhibitoryfeedback loop between populations of principal neurons (e.g., MCs) andinhibitory interneurons (e.g., GCs), as illustrated in FIG. 12. Rapidonline learning progressively modifies the synaptic weights of thisnetwork, generating attractors that correctly classify even highlydegraded, noisy inputs, as described elsewhere herein. It should benoted that this feedback loop recruits interneurons during learning; tomodel similarity, a prerequisite for constructing hierarchicalrepresentations, these recruited populations are permitted to overlap intheir representation of similar input stimuli. This renders the networkmore sensitive to the statistics of sensory input, thereby requiringsignal conditioning if parameter retuning is to be avoided. As notedabove and as illustrated in FIG. 12, to focus on the statisticalregularization of sensory inputs to this learning network, we includeonly the feedforward portion of the core network in the presentsimulations, reading out regularization and intermediate classificationresults (i.e., the goodness of preprocessing index g_(p) and thresholdedHamming distances) directly from the interneuron population. As in thefull model described previously, sensor activation levels arerepresented in principal neurons by a spike phase code with respect toan underlying gamma oscillation, and we use an asymmetric STDP learningrule, referred to herein as a heterogeneous STDP (hSTDP) learning rule,to modify MC-to-GC synaptic weights.

Heterogeneity in model parameters. Heterogeneity is abundant in biology;information is commonly represented in populations of neurons withsimilar but not identical properties. This is often elided asunavoidable biological variability, but may in fact serve an importantcomputational purpose. For example, recent experimental studies in theretina have shown that the population code exhibited by a heterogeneousensemble of neurons is considerably more reliable than that of ahomogeneous ensemble. To assess and take advantage of this potential, wehere incorporate network heterogeneities in three ways:

1. Nonuniform sensor scaling: This process is part of the sensor scalingpreprocessor described above, employed to ensure feature valuedifferences among inputs.

2. Heterogeneous duplication: The heterogeneous duplication preprocessorfans out a common input stream to a heterogeneous population ofexcitatory feedforward interneurons, which then deliver this input to nsister MCs via sparse random projections, as previously described inconjunction with FIG. 4.

3. Model parameter heterogeneities: We assigned variable spikingthresholds to sister MCs and to GC interneurons. These partiallyredundant MC groups further enabled us to assign a wide range ofMC-to-GC synaptic connection densities across the core learning network.Finally, the maximum permitted synaptic weights w_(max) under the STDPrule were heterogeneous; we refer to this overall rule as an hSTDP rule.These heterogeneities render the post-signal conditioning learningnetwork more robust to statistically diverse datasets.

Heterogeneous spike timing-dependent plasticity (hSTDP) rule. Per thislearning rule, MC-to-GC excitatory synaptic weights were potentiatedwhen MC spikes preceded GC spikes; otherwise these synapses weredepressed. The hSTDP rule parameters a_(p), a_(m), tau_(p), tau_(m), andw_(scale) were tuned using a synthetic dataset, whereas the distributionof maximum synaptic weights w_(max) was tuned only once using avalidation set from Batch 1 of the UCSD chemosensor drift dataset.Training and testing with the additional datasets described herein alsoused this same instantiated, parameterized network.

Additional aspects of the testing of the present embodiments usingexperimental datasets will now be described.

The results presented here were generated using a common network withall hyperparameters predetermined except for the number of columns and,in one case, the number of GC interneurons per sensor. The number ofprocessing columns depended directly on the number of sensor inputsprovided by the dataset (input data dimensionality) multiplied by thedivergence ratio n of the heterogeneous duplication preprocessor (heldconstant at 5 for all simulations herein; FIG. 4). Excitatory synapticweights in the core network were plastic, governed by an hSTDP rule withfixed parameters as described above.

UCSD gas sensor drift dataset. We first applied our algorithm to thepublicly available UCSD gas sensor drift dataset, modestly reconfiguredto assess online learning. The dataset contains 13910 measurements intotal, taken from an array of 16 MOS chemosensors exposed to 6 gas-phaseodorants presented across a substantial range of concentrations (10-1000ppmv). It should be noted that these data were gathered in ten batchesover the course of three years; owing to sensor drift, the chemosensors'responses to odorants changed drastically over this timescale,presenting a challenge to classification algorithms that model orotherwise compensate for that drift. For the present embodiments, weused data from Batches 1 (sensor age 1-2 months) and 7 (sensor age 21months). As in previous work, we used only the peak sensor responses (16out of the available 128 features in the dataset) for training andtesting. To better assess online learning, we reconfigured the datasetinto six groups corresponding to the six gas types, and trained thenetwork with data from each of these six groups separately, in order.Consequently, each training set comprised 1-10 samples (for 1-shotthrough 10-shot learning, respectively) of the same odorant, at randomlyselected concentrations. After training on each odorant group, we testedall six odorants (at randomly selected concentrations) before proceedingto train the next group in the list, until the network had learned allsix odorants. Testing an odorant on which the network had not yet beentrained produced the classification result “none of the above”—animportant capability for “learning in the wild,” wherein many presentedodorants would be unfamiliar and should not be forced incorrectly intoexisting classes. For sensor scaling and parameter tuning for this andall subsequent data sets, we used 10% of the Batch 1 data as avalidation set. The six odorant groups, in the order of training,included ammonia (group 1), acetaldehyde (group 2), acetone (group 3),ethylene (group 4), ethanol (group 5), and toluene (group 6).

Forest type spectral mapping dataset. This dataset is designed toidentify forest types in Japan using spectral data from ASTER satelliteimagery. Each of the 326 samples includes 27 spectral features. We used10% of the data as a validation set for preprocessor scaling. Becausethe dataset included negative values, we also, prior to sensor scaling,subtracted the minimum values of each feature (as obtained from thevalidation set) to render most feature values positive; any remainingnegative data points were clipped to zero. To better assess onlinelearning, we split the dataset into 4 groups corresponding to the fourforest type classes, and trained with each of these groups in sequence:Sugi (group 1), Hinoki (group 2), Mixed deciduous (group 3), Other(group 4).

Species-specific anuran call dataset. This dataset includes acousticfeatures (mel frequency cepstral coefficients, MFCCs) extracted from thecall syllables of 10 different frog and toad species, recorded in thewild in Brazil and Argentina. The dataset includes 7195 samples, witheach sample comprising 22 MFCC features (values between −1 and 1), andexhibits significant class imbalance; i.e., the numbers of samplescorresponding to each class (species) differ substantially. To make alldata samples positive, we shifted each value by +1 so that each MFCCfeature was in the range 0 to 2.

This dataset, uniquely among those tested, also included multilabel,multiclass classification, enabling us to illustrate the algorithm'sinnate capacity for natural hierarchical representation. Specifically,while training was performed using only species information (10 groups),we also measured the classification of calls into the correct anurangenus and family. Altogether, the 10 species in the dataset comprise 8anuran genera within 4 families. 10% of the data were retained as avalidation set, although these data were not used because the featurerange was already known to be between 0 and 2 and hence validation perse was not required. As above, to assess online learning, we split thedataset into 10 groups corresponding to the 10 species, and trained witheach in series: Adenomera andre (family Leptodactylidae, group 1),Adenomera hylaedactylus (family Leptodactylidae, group 2), Ameeregatrivittata (family Dendrobatidae, group 3), Hyla minuta (sincereclassified as Dendropsophus minutus, family Hylidae, group 4),Hypsiboas cinerascens (family Hylidae, group 5), Hypsiboas cordobae(family Hylidae, group 6), Leptodactylus fuscus (family Leptodactylidae,group 7), Osteocephalus oophagus (family Hylidae, group 8), Rhinellagranulosa (family Bufonidae, group 9), Scinax ruber (family Hylidae,group 10).

After training the network with standard heterogeneous parameters, andtuning the w_(max) distribution on the validation set of batch 1 of theUCSD chemosensor drift dataset, we trained the algorithm and tested itsperformance on three different datasets as described above.Specifically, we measured (1) the goodness of preprocessing (g_(p)) foreach dataset, to assess how well the same instantiated, parameterizednetwork would operate across a statistically diverse range of inputs,and (2) an interim estimate of classification performance based on athresholded Hamming distance between activated ensembles in theinterneuron representation, omitting the recurrent feedback loop of thefull model, as illustrated in FIG. 12. The latter measure is used in thepresent embodiments in order to illustrate the importance of signalconditioning, and generally should not be used as a benchmark for theperformance of illustrative embodiments of the full algorithm, whichclassifies signals successfully under high levels of synthetic impulsenoise, as previously described herein.

An important feature for present purposes in the FIG. 12 embodiment isthe uniformity of interneuron recruitment levels across a statisticallydiverse set of raw input signals, as assessed by g_(p). Direct inputsfrom deployed sensors differ substantially. As the distribution ofresponse amplitudes across a sensor array strongly affects the efficacyof interneuron recruitment in this framework, and interneuronrecruitment profiles substantially determine learning and classificationperformance, input patterns in illustrative embodiments are transformedto exhibit a relatively consistent statistical structure in order toavoid the need to retune network parameters, and hence enable “learningin the wild.”

To assess preprocessor efficacy, we first implemented a 16-columnnetwork including 16 principal neurons (e.g., MCs) and 3200 inhibitoryinterneurons (e.g., GCs), and presented this network with Batch 1 datafrom the UCSD sensor drift dataset. Interneuron recruitment into theactive ensemble by these raw sensor inputs (after being linearly scaledby a factor of 5×10⁻⁵) differed substantially among samples and was zerofor some lower-concentration samples, resulting in a g_(p) value ofzero. Subsequent preprocessor stages regularize the distribution ofinput amplitudes and improve interneuron recruitment uniformity asreflected by g_(p).

Sensor scaling. Heterogeneous sensor arrays require sensor-specificrescaling to a common range so that sensors producing the largest outputranges do not inappropriately dominate network operations. Accordingly,in the first preprocessing step, we scaled both the training set and thetest set by the maximum observed sensor responses determined from the10% validation set of Batch 1 (uniform sensor scaling). We then furtherscaled all inputs by an equidimensional uniform vector v_(uni), wherev_(uni)∈[0.5, 1.0] (nonuniform sensor scaling). Sensor response profilesbecame more comparable in amplitude, but still exhibitconcentration-dependent activation profiles and less uniform interneuronrecruitment.

Unsupervised intensity normalization. Distinguishing concentrationdifferences from genuine quality differences in the biological system(concentration tolerance) depends in part on a global inhibitoryfeedback mechanism instantiated in the MOB glomerular layer. We appliedthis normalization operation to the output of the sensor scalingpreprocessor. The diverse sensor response profiles observed for the samegas types arise from concentration differences; this preprocessorsubstantially eliminates those within-type differences. Notably, thisstep removes the need to train the algorithm with multipleconcentrations of a given gas type, enabling generalization beyondexperience in the concentration domain.

Heterogeneous duplication. In this step, the output of the intensitynormalization preprocessor first is projected to a higher dimension in acolumn-specific manner by duplicating each output onto m feedforwardexcitatory interneurons with heterogeneous properties and then randomlyconnecting those interneurons to n principal neurons (e.g., MCs),thereby multiplying the number of columns of the subsequent corelearning network by a factor of n (column duplication). In the presentsimulations, m=n=5 (FIG. 4). After applying this preprocessing step,sensor response distributions become regularized and interneuronrecruitment becomes substantially uniform across samples, exhibiting ag_(p) of 0.94 for Batch 1 data. It should be noted that thistransformation occurs in a naturally online manner, without destroyinginherent similarity relationships among data samples or reducing testset classification performance.

These sequential preprocessor steps, which we refer to collectively assignal conditioning, ensure that statistically diverse inputs aretransformed so as to recruit comparable numbers of interneurons, andconsequently can be effectively learned and classified by the sameinstantiated, parameterized network.

UCSD gas sensor drift. Using these preprocessors, we tested the“learning in the wild” capability of our feedforward learning network,first using Batch 1 data, and then, without changing any networkparameters, Batch 7 data. We first trained the network on raw sensordata from Batch 1 using one-shot learning with odorant concentrationuncontrolled. In total, the training set constituted 1.35% of thedataset. As noted above, we trained on each group (odorant type) insequence, testing performance on all six groups at each step (withodorants from untrained groups generating “none of the above”classifications). Unsurprisingly, performance deteriorated aftertraining on two or more groups, with the average accuracy across alltraining stages being only 35.86%. Following the same trainingprocedure, but using a network incorporating the preprocessors andheterogeneities described above, we obtained a mean classificationaccuracy of 96.00%.

To assess the effects of heterogeneity per se, we next trained aseparate network, using the same parameters and including the threepreprocessors, but excluding parameter heterogeneity. Specifically, thisexclusion implied:

1. No modulation of sensor scaling parameters by an equidimensionalrandom vector.

2. No heterogeneity in the parameters of feedforward interneurons.

3. No heterogeneity in core learning network parameters.

In this scenario, the average performance across all 6 groups dropped to89.66%, largely owing to performance reductions in later-trained groups.Because of the generally high performance on Batch 1 data, we did notalso analyze performance with multiple-shot learning.

Later batches in the UCSD dataset exhibited responses to odorants thatdiffered sharply from those in earlier batches, owing to gradual sensorcontamination and other forms of drift. Because the practical goal of“learning in the wild” is to enable the same instantiated network tooperate effectively on statistically diverse datasets, we trained thesame network (identical parameters) on these Batch 7 data, whichcomprise odorant responses from the same sensors as in Batch 1, butfollowing 21 months of sensor degradation. It should be noted that thesequentially applied preprocessors, with heterogeneity, regularized thedistribution of sensor input amplitudes to a form consistent with thatof the processed Batch 1 data, resulting in a uniform recruitment ofinterneurons across samples and concentrations.

We trained this network using one-shot learning of randomly selectedBatch 7 samples (concentrations uncontrolled), using the same proceduresas for Batch 1. As with Batch 1, performance dropped rapidly asadditional groups were learned; the average performance across allstages of learning was 42.42%, with a training set comprising 0.17% ofthe data. After applying the three preprocessors, includingheterogeneities, average performance improved to 81.42%. Omittingheterogeneity as above reduced average performance to 77.38%.

We then trained the network using two-shot, five-shot, and 10 shotonline learning protocols. Training trials were grouped by odorantidentity to demonstrate online learning (i.e., not intercalated);concentrations again were uncontrolled. Classification accuracy improvedsubstantially with the additional training yielding a maximum of 91.10%average accuracy for 10-shot training. The 10-shot training setcomprised 1.7% of the Batch 7 data.

Forest type spectral maps. Despite being inspired by the neuralcircuitry of the MOB, this network was expected to perform comparablywell on datasets exhibiting structural properties similar to odorantstimuli: relatively high dimensionalities without low-dimensionalstructure such as that exhibited by visual images. To demonstrate this,and to test the capacities of our preprocessors to appropriatelyregularize the statistical structures of non-chemosensory datasets, wetested the same network utilized above on two additional datasets.

We first tested the algorithm's performance on a 27-dimensional datasetof hyperspectral mapping data derived from ASTER satellite imagery,intended to identify four classes of Japanese forest cover. The networkwas expanded from 16 input dimensions (for the UCSD dataset) to 27 inputcolumns to match dataset dimensionality, and included 200 granule cellsper sensor. Despite substantial differences in signal statistics, ourpreprocessor cascade regularized the input distribution and achievednear-uniform interneuron recruitment.

We trained the network with one shot of each of the four forest types;the training set consequently comprised 0.76% of the data (4 of 523samples), and the test set comprised 89.24% (463 of 523 samples). Theaverage classification accuracy across all groups was 82.03%. Because ofthe special status of the “other” group, “other” classifications werepooled with “none of the above” classifications after the network wastrained on all four groups. Performance improved after two-, five-, and10-shot training, reaching 88.39% after ten-shot learning (the trainingset here comprised 7.65% of the data). When we omitted networkheterogeneities, as with the UCSD chemosensory dataset, the averageaccuracy for one-shot learning dropped from 82.03% to 74.53%.

Species-specific anuran calls. Finally, we also tested the algorithm onan implicitly hierarchical classification task using a dataset derivedfrom a corpus of recordings of vocalizations from ten anuran species. Asdetailed above, the dataset comprised 22 mel frequency cepstralcoefficients describing the acoustic features of these call syllables.We sought to identify the animal species, but also the genus and family,associated with each call. To do this, we deployed a network withhyperparameters identical to those used in prior datasets, with twoexceptions. First, the network was necessarily sized for the 22 inputdimensions of the dataset. Second, the number of interneurons wasexpanded to 300 per sensor; this was necessary in order to adequatelylearn all ten classes without the ANE function of the fully intactnetwork described in conjunction with FIG. 2. As with the earlierdatasets, preprocessing yielded a consistent statistical distribution ofinput amplitudes and a near-uniform recruitment of interneurons.

One-shot online learning of the ten groups (species) in this datasetyielded somewhat poorer classification accuracy than in the previousdatasets tested; the accuracy across groups averaged 75.72%, with thetraining set size comprising just 0.14% of the dataset (10 of 7195samples). Expanding to two- and five-shot training produced littleimprovement. However, expansion to 10-shot training improvedclassification accuracy to 93.25%, with the training set comprising1.39% of the data (100 of 7195 samples). Removing parameterheterogeneity reduced 10-shot classification performance to 90.54%.

Finally, we assessed classification performance with respect to theeight anuran genera and four families embedding the ten species on whichthe network was trained. No additional training or network design wasperformed; output was simply reclassified with respect to these highercladistic levels. Performance on this classification task largelytracked that of classifying by species, with accuracy increasingsubstantially given 10-shot training and being modestly impaired by theremoval of network heterogeneity. This implicit capacity to respecthierarchical similarity relationships is a substantial benefit of thegeneralized, similarity-representing variant of this algorithm asdescribed herein.

Some “learning in the wild” embodiments herein illustratively comprise aset of capacities for artificial networks that reflect the performanceof biological systems operating in natural environments. Most of thedifficult challenges in the “learning in the wild” context arise from asharply limited ability to regulate the stimuli presented by theexternal environment, whether in their unpredictable diversity, theirinterference with one another, or their intrinsic variances. A givenillustrative embodiment disclosed herein has one or more of thefollowing advantageous features:

1. Robust to “wild,” poorly-matched inputs without resorting tohyperparameter re-tuning.

2. Robust to environmental and stimulus variance, includingunpredictable stimulus intensities (e.g., odorant concentrations), otherforms of stimulus heterogeneity, and the effects of environmentaltemperature and humidity.

3. Exhibits concentration tolerance where appropriate, and also providean estimate of concentration.

4. Robust to missing or noisy sensor data, and to unlabeled trainingsets.

5. Exhibits rapid, semi-supervised or unsupervised, one- or few-shotlearning of novel stimuli.

6. Supports online learning (no catastrophic forgetting, no need tostore trained data).

7. Adapts to sensor drift owing to time and/or contamination.

8. Provides a “none of the above” option during classification(classifier confidence).

9. Identifies the signatures of known inputs despite substantialinterference from background stimuli (whether previously orsimultaneously delivered).

Some embodiments disclosed herein exhibit all or a majority of theseadvantageous properties. For example, in illustrative embodiments, wehave configured the network's rapid learning capabilities to achieve apractical solution to the problem of sensor drift and generalized thealgorithm to embed an explicit representation of similarity so as toenable support for hierarchical clustering. A preliminary example ofthis capacity is illustrated here in the classification of anuran callswith respect to species, genus, and family. This generalizedimplementation of the algorithm, however, becomes necessarily moresensitive to the statistical structure of sensory inputs. We here haveoutlined a signal conditioning solution in which wild sensory inputs areregularized by a series of preprocessors modeled on the features andcircuits of the MOB glomerular layer. Consequently, a singleinstantiated network is capable of productively learning and classifyingwidely heterogeneous sets of input stimuli.

Data normalization in some form is a common procedure in non-SNNs. Insome embodiments herein, we implement a data regularization procedurefor SNNs that is compatible with rapid learning, localized brain-mimeticcomputational principles, and “learning in the wild” constraints.Notably, under these constraints, samples may be rare, and batch sizessmall, such that aggregate data features such as means and standarddeviations are difficult to ascertain. We further ensure that singleinstantiated networks could effectively learn and classify a widediversity of datasets. The successive preprocessors described hereintransformed four different datasets with different patterns of internalsample diversity into a common statistical form, such that the samenetwork could effectively operate on them all without the need forhyperparameter retuning.

The final preprocessor in the sequence, heterogeneous duplication (FIG.4), is a statistical regularization algorithm based on the properties ofsparse random projections. Interestingly, its implementation closelyadheres to an anatomical circuit motif within MOB intraglomerularnetworks, to which function has yet to be attributed. The need forstatistical regularization of input patterns in this way has not yetbeen recognized in the literature on biological olfaction (except in thespecific case of concentration), so it is an interesting possibilitythat this network motif may present a solution to a previouslyunrecognized neurophysiological problem.

The simulations described in conjunction with the present embodimentsconcern the initial preprocessing steps and first feed-forwardprojection of the biomimetic algorithm (FIG. 12; corresponding to theEPLff component described previously), omitting the dynamical spiketiming-based attractor functionality of the full network in favor of acloser examination of preprocessor properties. Accordingly, the metricsof greatest interest are the uniformity of interneuron recruitment and apreliminary estimate of classification performance based on the Hammingdistances calculated between interneuronal activation patterns. Thelatter metric, in particular, should not be confused with theperformance of a fully implemented brain-mimetic implementation, of thetype described elsewhere herein; obtaining optimized classificationaccuracy was not the primary purpose of this reduced network. Amongother limitations, the Hamming distance metric cannot accommodate theANE method, by which new interneurons are dynamically added to thenetwork after the fashion of adult neurogenesis in the MOB, as describedelsewhere herein, because ANE alters the dimensionality of the space inwhich the Hamming distance is calculated. Owing to the absence of ANE,the present network's performance begins to drop off as the number oflearned stimuli increases. The average performance values, accordingly,are underestimates of the performance of the fully intact networkdescribed in conjunction with FIG. 2.

The present embodiments illustrate that a series of preprocessing steps,modeled after particular attributes of the mammalian MOB, successfullyconditions statistically diverse input signals from both chemosensoryand non-chemosensory sources, such that a single instantiated,parameterized network can rapidly learn and successfully classify thesesignals. We have termed this robustness to uncontrolled environmentalvariance “learning in the wild.” This is an important capability forfield-deployed devices expected to process and identify similarlydiverse sensory signatures within unregulated environments. Moreover, aswith the intact network described in conjunction with FIG. 2, thesepreprocessor algorithms were implemented using localized computationaland plasticity rules and hence are amenable to implementation onneuromorphic hardware platforms.

It should also be understood that the particular arrangements shown anddescribed in conjunction with FIGS. 1 through 12 are presented by way ofillustrative example only, and numerous alternative embodiments arepossible. The various embodiments disclosed herein should therefore notbe construed as limiting in any way. Numerous alternative arrangementsof neuromorphic algorithms can be utilized in other embodiments. Thoseskilled in the art will also recognize that alternative processingoperations and associated system entity configurations can be used inother embodiments.

It is therefore possible that other embodiments may include additionalor alternative system elements, relative to the entities of theillustrative embodiments. Accordingly, the particular systemconfigurations and associated algorithm implementations can be varied inother embodiments.

A given processing device or other component of an informationprocessing system as described herein is illustratively configuredutilizing a corresponding processing device comprising a processorcoupled to a memory. The processor executes software program code storedin the memory in order to control the performance of processingoperations and other functionality. The processing device also comprisesa network interface that supports communication over one or morenetworks.

The processor may comprise, for example, a neuromorphic processor, amicroprocessor, an ASIC, an FPGA, a CPU, an ALU, a GPU, a DSP, or othersimilar processing device component, as well as other types andarrangements of processing circuitry, in any combination. For example, agiven processing device as disclosed herein can be implemented usingsuch circuitry.

The memory stores software program code for execution by the processorin implementing portions of the functionality of the processing device.A given such memory that stores such program code for execution by acorresponding processor is an example of what is more generally referredto herein as a processor-readable storage medium having program codeembodied therein, and may comprise, for example, electronic memory suchas SRAM, DRAM or other types of random access memory, ROM, flash memory,magnetic memory, optical memory, or other types of storage devices inany combination.

As mentioned previously, articles of manufacture comprising suchprocessor-readable storage media are considered embodiments of theinvention. The term “article of manufacture” as used herein should beunderstood to exclude transitory, propagating signals. Other types ofcomputer program products comprising processor-readable storage mediacan be implemented in other embodiments.

In addition, embodiments of the invention may be implemented in the formof integrated circuits comprising processing circuitry configured toimplement processing operations associated with implementation of aneuromorphic algorithm.

An information processing system as disclosed herein may be implementedusing one or more processing platforms, or portions thereof.

For example, one illustrative embodiment of a processing platform thatmay be used to implement at least a portion of an information processingsystem comprises cloud infrastructure including virtual machinesimplemented using a hypervisor that runs on physical infrastructure.Such virtual machines may comprise respective processing devices thatcommunicate with one another over one or more networks.

The cloud infrastructure in such an embodiment may further comprise oneor more sets of applications running on respective ones of the virtualmachines under the control of the hypervisor. It is also possible to usemultiple hypervisors each providing a set of virtual machines using atleast one underlying physical machine. Different sets of virtualmachines provided by one or more hypervisors may be utilized inconfiguring multiple instances of various components of the informationprocessing system.

Another illustrative embodiment of a processing platform that may beused to implement at least a portion of an information processing systemas disclosed herein comprises a plurality of processing devices whichcommunicate with one another over at least one network. Each processingdevice of the processing platform is assumed to comprise a processorcoupled to a memory.

Again, these particular processing platforms are presented by way ofexample only, and an information processing system may includeadditional or alternative processing platforms, as well as numerousdistinct processing platforms in any combination, with each suchplatform comprising one or more computers, servers, storage devices orother processing devices.

A given processing platform implementing a neuromorphic algorithm asdisclosed herein can alternatively comprise a single processing device,such as a computer, mobile telephone or handheld sensor device, thatimplements not only the neuromorphic algorithm but also a sensor arrayand one or more controlled components. It is also possible in someembodiments that one or more such system elements can run on or beotherwise supported by cloud infrastructure or other types ofvirtualization infrastructure.

It should therefore be understood that in other embodiments differentarrangements of additional or alternative elements may be used. At leasta subset of these elements may be collectively implemented on a commonprocessing platform, or each such element may be implemented on aseparate processing platform.

Also, numerous other arrangements of computers, servers, storage devicesor other components are possible in an information processing system.Such components can communicate with other elements of the informationprocessing system over any type of network or other communication media.

As indicated previously, components of the system as disclosed hereincan be implemented at least in part in the form of one or more softwareprograms stored in memory and executed by a processor of a processingdevice. For example, certain functionality disclosed herein can beimplemented at least in part in the form of software.

The particular configurations of information processing systemsdescribed herein are exemplary only, and a given such system in otherembodiments may include other elements in addition to or in place ofthose specifically shown, including one or more elements of a typecommonly found in a conventional implementation of such a system.

For example, in some embodiments, an information processing system maybe configured to utilize the disclosed techniques to provide additionalor alternative functionality in other contexts.

It should again be emphasized that the embodiments of the invention asdescribed herein are intended to be illustrative only. Other embodimentsof the invention can be implemented utilizing a wide variety ofdifferent types and arrangements of information processing systems,networks and processing devices than those utilized in the particularillustrative embodiments described herein, and in numerous alternativeprocessing contexts. In addition, the particular assumptions made hereinin the context of describing certain embodiments need not apply in otherembodiments. These and numerous other alternative embodiments will bereadily apparent to those skilled in the art.

1. A computer-implemented method of training a neural network torecognize sensory patterns, the method comprising: obtaining input data;preprocessing the input data in one or more preprocessors of the neuralnetwork; applying the preprocessed input data to a core portion of theneural network, the core portion of the neural network comprising aplurality of principal neurons and a plurality of interneurons, the coreportion of the neural network implementing a feedback loop from theinterneurons to the principal neurons that supports persistentunsupervised differentiation of multiple learned sensory patterns overtime; obtaining an output from the core portion of the neural network;and performing at least one automated action based at least in part onthe output obtained from the core portion of the neural network; whereinthe method is performed by at least one processing device comprising aprocessor coupled to a memory.
 2. The method of claim 1 wherein theneural network comprises a spiking neural network (SNN).
 3. The methodof claim 2 wherein the SNN is configured to provide spike timing for thefeedback loop with inhibition delaying the spike timing and relativelystrong sensory input advancing the spike timing.
 4. The method of claim3 wherein the feedback loop is configured to adapt synaptic weights ofthe core network and operation of the feedback loop in adapting thesynaptic weights is controlled based at least in part on spike timinginformation represented by relative timing of spikes for at least aportion of the principal neurons and the interneurons.
 5. The method ofclaim 1 at least a subset of the principal neurons of the core portionof the neural network are configured to represent respective mitralcells of an olfactory learning system and at least a subset of theinterneurons of the core portion of the neural network are configured torepresent respective granule cells of the olfactory learning system. 6.The method of claim 1 further comprising adaptively expanding the neuralnetwork by incorporating additional interneurons into to one or more of:(i) at least one of the one or more preprocessors of the neural network;and (ii) the core portion of the neural network.
 7. The method of claim6 wherein the additional interneurons are incorporated into the coreportion of the neural network in a manner that does not disrupt existinglearned sensory patterns of the core portion of the neural network. 8.The method of claim 1 wherein obtaining input data comprises obtainingthe input data from one or more sensors.
 9. The method of claim 1wherein a given one of the one or more preprocessors of the neuralnetwork comprises a plurality of input nodes each adapted to receiveinput data associated with a different data source.
 10. The method ofclaim 9 wherein the input nodes are adapted to receive input data fromrespective different sensors.
 11. The method of claim 9 wherein thegiven preprocessor of the neural network comprises a heterogeneousduplication preprocessor configured to statistically regularize diversesensory inputs of the obtained input data.
 12. The method of claim 9wherein the given preprocessor of the neural network further comprisesfor a particular one of the input nodes: a plurality of excitatoryfeed-forward interneurons each coupled to the particular input node; anda plurality of principal neurons each coupled to one or more of theexcitatory feed-forward interneurons.
 13. The method of claim 1 whereinthe core portion of the neural network comprises a synaptic interactionmatrix of the principal neurons and the interneurons in which ann-dimensional representation in the principal neurons is mapped to anm-dimensional representation in the interneurons, where m>>n.
 14. Themethod of claim 1 wherein the neural network further comprises aneuromodulatory dynamic state trajectory configured to adjust neuronalproperties systematically and select a particular outcome.
 15. Themethod of claim 1 wherein the neural network further comprises aninference network arranged between the principal neurons and theinterneurons and configured to deliver input to the interneurons thatinfluences how the interneurons affect the principal neurons such thatthe principal neurons thereby exert different effects on theinterneurons and the inference network.
 16. The method of claim 1wherein multiple cycles of the feedback loop are executed within asingle cycle of a data sampling loop utilized in obtaining the inputdata.
 17. The method of claim 1 wherein the feedback loop is configuredto control delivery of synaptic inhibition information from theinterneurons of the core portion back to the principal neurons of thecore portion based at least in part on synaptic excitatory informationdelivered from the principal neurons to the interneurons.
 18. A systemcomprising: at least one processing device comprising a processorcoupled to a memory; the processing device being configured: to obtaininput data; to preprocess the input data in one or more preprocessors ofa neural network; to apply the preprocessed input data to a core portionof the neural network, the core portion of the neural network comprisinga plurality of principal neurons and a plurality of interneurons, thecore portion of the neural network implementing a feedback loop from theinterneurons to the principal neurons that supports persistentunsupervised differentiation of multiple learned sensory patterns overtime; to obtain an output from the core portion of the neural network;and to perform at least one automated action based at least in part onthe output obtained from the core portion of the neural network.
 19. Thesystem of claim 18 wherein the processing device is further configuredto adaptively expand the neural network by incorporating additionalinterneurons into one or more of: (i) at least one of the one or morepreprocessors of the neural network; and (ii) the core portion of theneural network.
 20. The system of claim 18 wherein the core portion ofthe neural network comprises a synaptic interaction matrix of theprincipal neurons and the interneurons in which an n-dimensionalrepresentation in the principal neurons is mapped to an m-dimensionalrepresentation in the interneurons, where m>>n.
 21. A computer programproduct comprising a non-transitory processor-readable storage mediumhaving stored therein program code of one or more software programs,wherein the program code, when executed by at least one processingdevice comprising a processor coupled to a memory, causes the processingdevice: to obtain input data; to preprocess the input data in one ormore preprocessors of a neural network; to apply the preprocessed inputdata to a core portion of the neural network, the core portion of theneural network comprising a plurality of principal neurons and aplurality of interneurons, the core portion of the neural networkimplementing a feedback loop from the interneurons to the principalneurons that supports persistent unsupervised differentiation ofmultiple learned sensory patterns over time; to obtain an output fromthe core portion of the neural network; and to perform at least oneautomated action based at least in part on the output obtained from thecore portion of the neural network.
 22. The computer program product ofclaim 21 wherein the program code when executed further causes theprocessing device to adaptively expand the neural network byincorporating additional interneurons into one or more of: (i) at leastone of the one or more preprocessors of the neural network; and (ii) thecore portion of the neural network.
 23. The computer program product ofclaim 21 wherein the core portion of the neural network comprises asynaptic interaction matrix of the principal neurons and theinterneurons in which an n-dimensional representation in the principalneurons is mapped to an m-dimensional representation in theinterneurons, where m>>n.
 24. The method of claim 1 wherein the one ormore preprocessors of the neural network comprise at least one layerthat includes a plurality of neurons of a first type and a plurality ofneurons of a second type different than the first type, and furtherwherein at least a subset of the neurons of the second type areconfigured to inhibit at least a subset of the neurons of the firsttype.
 25. The method of claim 24 wherein said at least one layer isconfigured to represent at least one glomerular layer of an olfactorylearning system, the neurons of the first type are configured torepresent respective external tufted (ET) cells of the olfactorylearning system, and the neurons of the second type are configured torepresent respective periglomerular (PG) cells of the olfactory learningsystem.
 26. The method of claim 24 wherein the inhibition of at least asubset of the neurons of the first type by at least a subset of theneurons of the second type comprises a graded lateral inhibition. 27.The method of claim 1 wherein the one or more preprocessors of theneural network comprise at least one concentration tolerancepreprocessor configured to limit concentration-specific variance inoutputs generated in response to respective different instances of inputdata.
 28. The method of claim 1 wherein the one or more preprocessors ofthe neural network comprise at least one sensor scaling preprocessorconfigured to rescale outputs of multiple heterogeneous sensors suchthat corresponding inputs to the core portion of the neural network arestatistically similarly scaled.
 29. The method of claim 1 furthercomprising adding one or more neurons to the neural network withoutdisrupting an existing learned pattern obtained through previoustraining of the neural network.
 30. The method of claim 1 wherein theneural network is configured to implement online learning in which oneor more new patterns are learned with a size of the neural networkdynamically expanded, relative to a previous size of the neural network,without impairing one or more previous learned patterns of the neuralnetwork.